The speed of the cat when it slid off the table would be 4.43 m/s.
What is speed?Speed is defined as the rate of motion or action, or the rate of change of something. It is typically measured in terms of distance over time, such as kilometers per hour (km/h) or miles per hour (mph). Speed can also be expressed in terms of velocity, which is the rate of change in position. Velocity is measured in meters per second (m/s). In physics, speed is a scalar quantity, meaning it is a magnitude, or numerical value, without direction.
The speed of the cat can be calculated using the equation v^2=2gh, where v is the speed, g is the acceleration due to gravity (9.81 m/s^2), h is the height of the table (1.0 m).
So, the speed of the cat when it slid off the table would be:
v = sqrt(2*9.81*1.0) = 4.43 m/s
To learn more about speed
https://brainly.com/question/3004254
#SPJ1
Suppose we want to calculate the moment of inertia of a 59.5 kg skater, relative to vertical axis through their center of mass _ Part (a) First calculate the moment of inertia (in kg m when the skater has their arms pulled inward by assuming they are cylinder of radius 0.135 m Numeric A numeric value is expected and not an expression_ Ib Part (b) Now calculate the moment of inertia of the skater (in kgm?) with their arms extended by assuming that each arm is 5% of the mass of their body _ Assume the body is cylinder of the same size, and the arms are 0.975 m long rods extending straight out from their body being rotated at the ends Numeric A numeric value is expected and not an expression.
Part a: The moment of inertia when the skater dragged his or her arm inward is 0.542 kg-m².
Part b: Its moment of inertia is therefore 2.368 kg/m², if the skater's body is imagined to be a cylinder of same size.
Explain about the moment of inertia?The term "moment of inertia" refers to a physical quantity that quantifies a body's resistance to having their speed of rotation along an axis changed by the deployment of such a torque (turning force).
Part a:
Assuming the skater's arms are a cylinder of radius, when the skater's arms are dragged inward; R = 0.135 m
Moment of inertia; I = ?
The moment of inertia for the a cylindrical body is calculated using the parallel axis theorem:
I = 1/2 MR²
M is for mass, R is for radius, etc.
I = 1/2* 59.5*0.135²
I = 0.542
Hence, if the skater is a cylinder, the moment of inertia when the skater dragged his or her arm inward is 0.542 kg-m².
Part b:
Assuming that the mass of each arm equals 5% of the body mass of the skater with their arms extended:
The mass of each arm:
Ma = 0.05*M
Ma = 0.05*59.5 = 2.975
Residual mass;
Mb = M - 2Ma
Mb = 59.5 - 2*2.975
Mb = 53.55 kg
Suppose the arms be 0.875 m in length rods that reach straight from the body and are turned at the ends. The body is just a cylinder of same size.
Length of arm; 0.975 m
The moment of inertia about just the vertical axis is defined by the parallel axis theorem as:
I = 1/2MbR² + 2/3MaL²
I = 1/2*53.55*(0.135)² + 2/3*2.975*(0.975)²
I = 0.488 + 1.88
On simplification:
I = 2.368
Its moment of inertia is therefore 2.368 kg/m², if the skater's body is imagined to be a cylinder of same size and the arms to be straight rods that are rotated at the ends of the body.
To know more about the moment of inertia, here
https://brainly.com/question/14460640
#SPJ1
How can living things provide evidence for evolution?
Answer:
according to the variations that they have been within years.
Explanation:
Answer:
your answer is
Explanation:
Living things provide evidence for evolution through various ways such as the existence of homologous structures (similar structures in different organisms indicating a common ancestor), vestigial structures (organs that have lost their original function over time), the distribution of species across different regions, genetic similarities and differences between organisms, and the observation of natural selection in action.
a building is being knocked down with a wrecking ball, which is a big metal sphere that swings on a 14-m -long cable. you are (unwisely!) standing directly beneath the point from which the wrecking ball is hung when you notice that the ball has just been released and is swinging directly toward you.
Answer:
Explanation:
The type of motion executed will be the simple harmonic motion. The time do you have to move out of the way will be 1.74 sec.
What is simple harmonic motion?
When an object executes a to and fro motion in the definite plane when it is tied with the string. The type of motion will be the simple harmonic motion.
Simple harmonic motion is a form of periodic motion in mechanics and physics in which the restoring force on the moving item is directly proportional to the size of the object.
The time period is given by the formula;
Hence the time do you have to move out of the way will be 1.74 sec.
To learn more about the simple harmonic motion refer to the link;
brainly.com/question/17315536
Which electromagnet is the strongest?
An illustration of a metal bar with a coil of wire around it.
An illustration of a metal bar with a coil of wire around it it has more coils.
An illustration of a metal bar with a coil of wire around it it has less coils.
* The Answer is the 2nd picture - An illustration of a metal bar with a coil of wire around it it has more coils.
Therefore, of the three options given, the electromagnet with more coils around the metal rod is the most powerful if all other factors such as current and core material are kept constant.
What is the very short response to an electromagnet?
An electromagnet is a temporary magnet made by winding a wire around an iron core. When current flows through the coil, iron becomes a magnet, and when the current is cut off, it loses its magnetic properties.
What is Electromagnetism?
Electromagnetism is the branch of physics that deals with the electromagnetic forces that occur between charged particles. Electromagnetic force is one of the four basic forces and describes the electromagnetic field.
To know more about electromagnet visit:
https://brainly.com/question/17057080
#SPJ1
Answer: The answer is B
Explanation:
now consider the children's linear accelerations. which of the following statements are correct? check all that apply. view available hint(s)for part b now consider the children's linear accelerations. which of the following statements are correct?check all that apply. the last child in the line has the greatest tangential acceleration. the last child in the line has the greatest radial acceleration. all the children have the same tangential acceleration. all the children have the same radial acceleration.
The correct statements for the children's linear accelerations are:
The last child in the line has the greatest radial acceleration.All the children have the same tangential acceleration.How to determine factors of linear acceleration?Since the children are moving in a circle with a constant speed, their tangential acceleration is constant and equal for all of them. However, their radial acceleration depends on their distance from the center of the circle, and it decreases as the distance increases.
Therefore: The last child in the line has the greatest radial acceleration, since they are closest to the center of the circle. All the children have the same tangential acceleration.
Learn more on linear acceleration here: https://brainly.com/question/15411328
#SPJ1
What is determined by calculating the slope of the position vs time graph? position velocity distance displacemen
A crane is oriented so that the end of the 25-m boom AO lies in the yz plane. At the instant shown, the tension in cable AB is 5.9 kN Determine the moment about each of the coordinate axes of the force exerted on A by cable AB.
Previous question
0Nm, 147.5 Nm and -147.5Nm are the moment about each of the coordinate axes of the force exerted on A by cable AB.
What is moment?A moment is indeed a mathematical term used in physics that involves the combination of a physical quantity and a distance. Seconds relate to physical quantities that are dispersed from either the reference point and are often described with regard to something like a fixed reference point.
The instant therefore explains the position or arrangement of the amount. For instance, the moment of force, also known as torque, is the result of the force acting on an object and the item's distance first from reference point.
Moment = force ×distance
M = f × d
Moment about the x axis:
M = 5.9 ×0
M = 0Nm
Moment about the y axis:
M =5.9 ×25 = 147.5 Nm
Moment about the z axis:
M = 5.9 × (-25)
M = -147.5Nm
Therefore, 0Nm, 147.5 Nm and -147.5Nm are the moment about each of the coordinate axes of the force exerted on A by cable AB.
To learn more about moment, here:
https://brainly.com/question/1743527
#SPJ1
A region of space contains a uniform electric figure. Which statement about this situation is field, directed toward the right, as shown in the correct? a. The potential at all three locations is the same. b. The potentials at points A and B are equal, and the potential at point C is higher than the potential at point A c. The potential at points A and B are equal, and the potential at point C is lower than the potential at point A. d. The potential at point A is the highest, the potential at point B is the second highest, and the potential at point C is the lowest E) There is no measurable potential at any of these points
The right statement for electric field is The potential at points A and B are equal, and the potential at point C is lower than the potential at point A. The correct option to this question is C.
Electric field At a particular area, a uniform magnetic field and an equally uniform electric field act in the same direction. As an electron is projected into the area, it points its velocity in the direction of the fields.The field lines are parallel, uniformly spaced, and straight in an even electric field. Since a line can never begin and end on the same charge, electric field lines can never form closed loops. Always moving from higher potential to lesser potential, these field lines.For more information on electric field kindly visit to
https://brainly.com/question/8971780
#SPJ1
I need pls with this work pls
The missing part of the question have been filled below on Continental drift
What did Wegener do?
In the early part of the 20th century, a German scientist named Alfred Wegener, proposed the theory of continental drift which suggested the continents move and started out in different positions from what they are currently. In the 1960s, scientists discovered the spreading apart of areas of the sea floor. This in turn led to the theory of plate tectonics. The lithosphere is made of plates which float on a "plastic-like" undersurface called the mantle. Where these plates come together at boundaries, changes take place in the crust and its feature.
Read more on continental drift here:https://brainly.com/question/394265
#SPJ1
what is the net electric potential at the origin due to the circular arc of charge Q1 = +7.21 pC and the two particles of charges Q2 = 4.00Q1 and Q3 = −2.00Q1? The arc's center of curvature is at the origin and its radius is R=2.00 m; the angle indicated is θ=20.0∘
The net electric potential at the origin due to the circular arc of charge Q1, and the two particles of charges Q2 and Q3 can be calculated by using the formula for electric potential due to a point charge:
V = (kQ)/r
Where V is the electric potential, k is the Coulomb's constant (8.99 x 10^9 Nm^2/C^2), Q is the charge, and r is the distance from the point of charge to the point where we want to calculate the electric potential.
For the circular arc of charge Q1, the electric potential at the origin is:
V1 = (kQ1)/R = (8.99 x 10^9 Nm^2/C^2)(7.21 x 10^-12 C)/(2.00 m) = 1.62 x 10^-2 V
For the particle of charge Q2, the electric potential at the origin is:
V2 = (kQ2)/R = (8.99 x 10^9 Nm^2/C^2)(4.00Q1)/(2.00 m) = 4.00V1 = 6.48 x 10^-2 V
For the particle of charge Q3, the electric potential at the origin is:
V3 = (kQ3)/R = (8.99 x 10^9 Nm^2/C^2)(-2.00Q1)/(2.00 m) = -2.00V1 = -3.24 x 10^-2 V
The net electric potential at the origin is the sum of the electric potentials due to each charge:
Vnet = V1 + V2 + V3 = 1.62 x 10^-2 V + 6.48 x 10^-2 V - 3.24 x 10^-2 V
Vnet = 4.86 x 10^-2 V
Therefore, the net electric potential at the origin due to the circular arc of charge Q1 and the two particles of charges Q2 and Q3 is 4.86 x 10^-2 V.
#SPJ1
Similar Question: https://brainly.com/question/8233653
A 1.67m wooden beam that weighs 100 pounds is resting on two supports. The first support is 0.2 m from one end of the beam, and the second support is 0.3 m from the other end. Assume the axis of rotation would be the center of the beam
a. Find the torques acting on the wooden beam
b. Find the net torque acting on the wooden beam
The torque acts on a distance of 0.2 m from one end of the beam is 88.96 Nm and the torque acting upon a the distance of 0.3 m from the other end of the beam is 133.4 Nm. Then, the net torque of the mass is 44.48 Nm.
What is torque ?Torque is the rotational analogue of force on an object. It is the measure of force that acts on the object to rotate the object about an axis.
It is the cross product of force and distance from the end of axis. Torques generates the angular momentum in the object.
Given the mass m= 100 pounds.
1 pound = 4.448 N
then Force by the weight F = 100 × 4.448 = 444.8 N.
Then, the torque acts over 0.2 m from one end = F .r = 444.8 × 0.2 = 88.96 Nm.
Then, the torque acts over 0.3 m from one end = F .r = 444.8 × 0.3 = 133.4 Nm.
Therefore, the net torque acting on the mass is 133.4 -88.96 = 44.48 Nm.
Find more on torques:
https://brainly.com/question/29024338
#SPJ1
A wave connected armature winding has V1 slots with 54 conductors per slot. If the flux per pole is 0.025 Wb and number of poles is 8, Find the speed at which generator should be run to give 513 V. Also find the speed If the armature is lap connected.
The required speed if the armature is lap connected is approximately 1425 RPS.
What is wavelength?Wavelength is a fundamental property of waves, including electromagnetic waves like light and radio waves, as well as other types of waves, such as sound waves or water waves.
Here,
To find the speed at which the generator should be run to give an output voltage of 513 V, we can use the formula:
E = 4.44 * f * N * φ * Z
First, let's find the value of Z,
Z = V₁ * Nc
Z = V₁ * slots * conductors per slot
Z = V₁ * 54
Substituting the given values, we get,
513 = 4.44 * f * N * 0.025 * V₁ * 54
Simplifying, we get:
N = 513 / (4.44 * f * 0.025 * V₁ * 54)
Substituting f = 50 Hz, and V₁ = 1, we get:
N = 513 / (4.44 * 50 * 0.025 * 54)
N ≈ 1.71 RPS
Therefore, the speed at which the generator should be run to give an output voltage of 513 V is approximately 1.71 RPS.
Now, to find the speed if the armature is lap connected, we can use the formula,
E = 2 * p * φ * N * Z / 60A
For a lap winding, A = p.
Substituting the given values, we get,
513 = 2 * 8 * 0.025 * N * V1 * 54 / (60 * 8)
N = 513 * 60 / (2 * 8 * 0.025 * V1 * 54)
Substituting V₁ = 1, we get:
N = 513 * 60 / (2 * 8 * 0.025 * 54)
N ≈ 1425RPS
Therefore, the speed of the armature is lap connected is approximately 1425 RPS.
Learn more about wavelength here:
https://brainly.com/question/13533093
#SPJ9
Terry kicks a soccer ball that is sitting motionless on the field. What is the best description of the energy transfer?(1 point).
When Terry kicks a soccer ball that is sitting motionless on the field, the energy transfer that occurs is from Terry's foot to the soccer ball. The transfer of energy can be described as kinetic energy, which is the energy an object possesses due to its motion.
What is kinetic energy?Kinetic energy is the energy that an object possesses due to its motion. It is defined as the energy an object has because of its mass and velocity.
Here,
With the ball being set in motion. This transfer of energy can be described as a transfer of kinetic energy. As the ball moves, it gains kinetic energy, which is the energy an object possesses by virtue of its motion. At the same time, Terry's foot loses kinetic energy. This is due to the conservation of energy, which states that energy can neither be created nor destroyed, only transferred or converted from one form to another. In this case, the energy that was initially in Terry's foot has been transferred to the ball in the form of kinetic energy, causing the ball to move.
Learn more about kinetic energy here:
https://brainly.com/question/22174271
#SPJ1
In both cases shown, a box is sliding across a floor with the same coefficient of kinetic friction and the same initial velocity The only difference between the two cases is the mass of the box. In which case will the box slide the furthest before coming to rest? a. Case 1 b. Same c. Case 2
The more frictional force is acting on greater mass. Hence, less it will be accelerated to significant distance. So that in case 1 with small mass will slide farthest.
What is friction ?Friction is the resistive force that hinder the motion of an object. It just opposes the normal force of an object. Thus, frictional force will have a negative sign always.
The force of exerted on an object is directly proportional to its mass. Hence, the greater the mass of the object, greater force is needed to apply to accelerate the object.
Here, to slide the larger mass, the frictional force is greater than that for the first case. However, the small mass can be moved to slide the surface furthest. Hence case 1 is correct.
Find more on friction:
https://brainly.com/question/28356847
#SPJ1
the half life of plutonium is 24000 years. how long does it take for the activity of plutonimum waste to decrease from 20000 to 625?
It takes approximately 61,649 years for the activity of plutonium waste to decrease from 20,000 to 625.
How to find the time it takes for the activity of plutonium waste to decrease.We can use the radioactive decay formula to find the time it takes for the activity of plutonium waste to decrease from 20,000 to 625:
A = A₀(1/2)^(t/T)
where
A₀ = initial activity (20,000)A = final activity (625)t = timeT = half-life (24,000 years)We can solve for t by taking the logarithm of both sides:
log(A/A₀) = -t/T × log(1/2)t/T = -log(A/A₀) / log(1/2)t = -T × log(A/A₀) / log(1/2)Substituting the values:
t = -24,000 years × log(625/20,000) / log(1/2)
t = 61,649 years
Therefore, it takes approximately 61,649 years for the activity of plutonium waste to decrease from 20,000 to 625.
Learn more about formula of decay here : brainly.com/question/29599279
#SPJ1
A nylon string on a tennis racket is under a tension of 290 N.
Part A: If its diameter is 1.00 mm, by how much is it lengthened from its untensioned length of 31.0 cm? Use ENylon=5.00×109N/m2
The nylon string on the tennis racket lengthens by approximately 0.97 cm.
Explain Nylon String.Nylon string is a type of string used in sports equipment such as tennis rackets, badminton rackets, and squash rackets. It is made of nylon fibers and is known for its durability, strength, and elasticity.
To calculate the elongation of the nylon string, we can use the equation for linear deformation under tension:
ΔL = (F * L) / (A * E)
where ΔL is the change in length, F is the tension force, L is the original length, A is the cross-sectional area, and E is the Young's modulus.
We are given the tension force, L, and E, but we need to calculate the cross-sectional area A. Since the diameter of the string is given, we can use the formula for the area of a circle to find A:
A = (π/4) * d^2
where d is the diameter.
Substituting in the values, we get:
A = (π/4) * (0.001 m)^2 = 7.85 x 10^-7 m^2
Now we can calculate the elongation:
ΔL = (290 N * 0.31 m) / (7.85 x 10^-7 m^2 * 5.00 x 10^9 N/m^2) = 0.0097 m or 0.97 cm (to 2 significant figures)
Learn more about nylon string here:
https://brainly.com/question/15093344
#SPJ1
PLEAS HELP
The picture is to answer the questions and here are the questions
The Death of Georgi Markov and the Attack on Vladimir Kostov (1978)
1. What was the delivery method of the ricin?
2. What are the symptoms of ricin poisoning?
3. How much ricin did they find in Markov?
Tylenol Tampering (1982)
1. How many people died?
2. What are the circumstances surrounding the deaths?
3. When/where did the tampering likely occur? How do they know?
4. What is the significance of this case?
kinetic energy of an object whose mass is 1Kg and it is moving at a velocity of 5m/s.
The kinetic energy of the object is: KE = 0.5 x 1 kg x (5 m/s)2
= 12.5 J
What is kinetic energy?Kinetic energy is the energy of motion. It is the energy an object has due to its motion. Kinetic energy can be defined as the energy an object has due to its mass and its velocity. Kinetic energy is measured in Joules (J). Kinetic energy increases with increasing mass and velocity of an object. When an object is at rest, it has zero kinetic energy. When an object is in motion, it has kinetic energy. Kinetic energy is a form of energy that is associated with the motion of an object. It is the energy that is stored in the movement of an object. Kinetic energy is one of the fundamental forms of energy, along with potential energy.
Kinetic energy is the energy possessed by an object due to its motion. It is a form of energy that can be calculated using the equation:
Kinetic energy (KE) = 0.5 x Mass (m) x Velocity (v)2
In this case, the mass of the object is 1 kg and its velocity is 5 m/s.
To learn more about kinetic energy
https://brainly.com/question/30285686
#SPJ1
If a force is applied when using a lever over 2 meters to move the object 1 meter, the distance over which the force is applied is called the _____.
The distance over which the force is applied when using a lever is called the effort distance.
What is force?Force is defined as the rate of change of momentum.
Here,
The distance over which the force is applied when using a lever is called the effort distance. It refers to the distance between the point where the effort is applied and the fulcrum of the lever. In the case we described, where a force is applied when using a lever over 2 meters to move an object 1 meter, the effort distance would be 2 meters. The load distance, on the other hand, refers to the distance between the fulcrum and the point where the load is applied. Understanding the relationship between the effort and load distances is crucial to determining the mechanical advantage of a lever system.
Learn more about force here:
https://brainly.com/question/13191643
#SPJ1
A reaction was predicted to produce 32. 4 grams of a compound. When the product was measured, there were only 26. 1 grams made. What is the percent yield of this reaction?.
The percent yield of this reaction is 80.6%. This means that only 80.6% of the predicted amount of the compound was actually produced, while the remaining 19.4% was lost due to incomplete reactions or other factors.
The percent yield can be calculated as follows:
percent yield = (actual yield / theoretical yield) x 100%
Substituting the given values, we get:
percent yield = (26.1 / 32.4) x 100%
percent yield = 0.806 x 100%
percent yield = 80.6%
A compound is a substance made up of two or more different elements that are chemically bonded together in a fixed ratio. This means that compounds have a unique chemical formula, which describes the types and numbers of atoms that make up the compound.
The properties of a compound are different from those of the individual elements that make it up. For example, water (H2O) is a compound made up of hydrogen and oxygen. Although hydrogen is a gas and oxygen is a gas, water is a liquid at room temperature. This is because the properties of a compound are determined by the arrangement of the atoms and the type of chemical bonds between them.
Compounds are important in many areas of physics, including materials science, chemical engineering, and electronics. They are used to make a wide range of products, from plastics and medicines to electronic devices and batteries. Understanding the properties and behavior of compounds is therefore essential for many areas of research and development.
To learn more about Compound visit here:
brainly.com/question/19458442
#SPJ4
this raboratory activity is broken up into four distinct parts so that the goals and variables of each part can be
observed separately.
In Part I, students manipulate the
observe a magnetic field.
In Part II, students manipulate the
objects to observe an electric field.
In Part III, students intentionally change the
generated.
In Part IV, students intentionally change the
magnetic field.
•and document the attraction with a magnet to
~ and document the attraction between the
and measure the electric current
•and observe the generation of a
Answer:
This raboratory activity is broken up into four distinct parts so that the goals and variables of each part can be observed separately. In Part I, students manipulate the observe a magnetic field. In Part II, students manipulate the objects to observe an electric field. In Part III, students intentionally change the generated. In Part IV, students intentionally change the magnetic field. •and document the attraction with a magnet to ~ and document the attraction between the and measure the electric current •and observe the generation of a
In Part I of this lab activity, students manipulate objects to observe a magnetic field. In Part II, they manipulate objects to observe an electric field. In Part III, they intentionally change the generated electric field. In Part IV, they intentionally change the magnetic field and document the attraction with a magnet to and document the attraction between the objects and measure the electric current and observe the generation of a magnetic field.
The laboratory activity contains four distinct parts related to magnetic fields and electric fields. It is designed to help high school students understand the fundamental principles of electricity and electromagnetism in physics. Students manipulate, observe, document, and measure in all parts of the activity to gain comprehensive exposure.
Explanation:The laboratory activity you're referring to is subdivided into four distinct parts, each focusing on different aspects of Physics related to magnetic fields and electric fields.
In Part I of the lab, students experiment with a magnet to understand the mechanics of a magnetic field. Part II shifts the focus onto electric fields where students manipulate various objects and document interactions.
For Part III and Part IV, students are required to measure the electrical current generated and observe the change in generation when different variables are intentionally altered in the magnetic field.
Overall, this activity offers comprehensive exposure to the fundamental principles of electromagnetism and electricity in physics.
Learn more about Magnetic and Electric fields here:https://brainly.com/question/19691357
#SPJ2
A ball moving at 11 m/s makes an off-center
elastic collision with another ball of equal
mass that is initially at rest. The incom-
ing ball is deflected at an angle of 29◦ from its
original direction of motion.
Find the speed of the first ball after the
collision.
Answer in units of m/s. Answer in units of
m/s
Answer:
8.65 m/s.
Explanation:
Let's use conservation of momentum and conservation of kinetic energy to solve this problem.
Since the two balls have equal masses, we can simplify the problem by assuming they are identical. Let's call the initial speed of the incoming ball v and the final speed of the outgoing ball v'.
Conservation of momentum tells us that the total momentum before the collision is equal to the total momentum after the collision:
mv = mv'cos(29°) + mv'sin(29°)
where m is the mass of each ball.
Conservation of kinetic energy tells us that the total kinetic energy before the collision is equal to the total kinetic energy after the collision:
(1/2)mv^2 = (1/2)mv'^2
We can solve the first equation for v' and substitute it into the second equation:
v' = v(1 - sin(29°)) / cos(29°)
(1/2)mv^2 = (1/2)m[v(1 - sin(29°)) / cos(29°)]^2
Solving for v', we get:
v' = v[1 - sin(29°)] / cos(29°)
v' = 8.65 m/s (to two decimal places)
Therefore, the speed of the first ball after the collision is 8.65 m/s.
If the normal force exerted on the rock as it slides through its lowest point (point b) is twice the weight of the rock, how much work did friction do on the rock as it moved from a to b?.
The work done by friction as the rock moves from point a to point b is equal in magnitude to the potential energy of the rock at point a, and it is negative because it acts in the opposite direction to the displacement of the rock
To determine how much work friction did on the rock as it moved from point a to point b, we need to first consider the forces acting on the rock and the work done by each force.
At point a, the rock has only potential energy due to its position above the ground. As it slides down the slope towards point b, the potential energy is converted to kinetic energy, and the rock gains speed.
The forces acting on the rock as it slides down the slope are:
The force of gravity acting downward, with a magnitude equal to the weight of the rock (mg).
The normal force acting perpendicular to the slope, which is equal in magnitude but opposite in direction to the force of gravity (2mg at point b).
The force of friction acting parallel to the slope, in the opposite direction to the motion of the rock.
Since the rock is sliding down the slope, the force of friction must be acting in the direction opposite to the motion, which means that the work done by friction is negative.
The work-energy principle states that the net work done on an object is equal to its change in kinetic energy. In this case, we can assume that the initial velocity of the rock at point a is zero, so its initial kinetic energy is also zero.
At point b, the rock has reached its maximum speed and all of its potential energy has been converted to kinetic energy. Therefore, the work done by gravity is equal to the change in potential energy:
[tex]mgh = (1/2)mv^2[/tex]
where m is the mass of the rock, g is the acceleration due to gravity, h is the vertical distance between points a and b, v is the speed of the rock at point b.
Solving for v, we get:
[tex]v = \sqrt{(2gh)}[/tex]
The work done by the normal force is zero, since it acts perpendicular to the displacement of the rock.
The work done by friction is given by:
[tex]W_{friction} = -f * d[/tex]
where f is the force of friction and d is the horizontal distance between points a and b.
To determine the force of friction, we can use the fact that it is equal in magnitude to the normal force multiplied by the coefficient of friction (μ):
f = μ * N
At point b, the normal force is twice the weight of the rock, so N = 2mg. The coefficient of friction is not given, so we cannot calculate the exact value of the work done by friction.
However, we can make some general observations about the work done by friction based on the information given. Since the normal force at point b is twice the weight of the rock, this implies that the slope is steeper at point b than it is at point a. This in turn implies that the force of friction at point b is greater than it is at point a. Therefore, we can conclude that the work done by friction is negative and that its magnitude is greater than zero.
Finally, we can use the work-energy principle to calculate the work done by friction:
[tex]W_{friction} = -mgh = -[(1/2)mv^2][/tex]
Substituting the expression we derived for v, we get:
[tex]W_{friction} = -mgh = -[(1/2)m(2gh)] = -mgh[/tex]
for such more question on friction
https://brainly.com/question/24338873
#SPJ4
A 6.0-kg rock is dropped from a height of 9.0 m. At what height is the rock's kinetic energy twice its potential energy?
Answer:
the height at which the rock's kinetic energy is twice its potential energy is approximately 4.5 m.
Explanation:
When the rock is dropped from a height of 9.0 m, it initially has potential energy equal to mgh, where m is the mass of the rock, g is the acceleration due to gravity (9.8 m/s^2), and h is the height from which the rock was dropped. Therefore, the potential energy of the rock is:
U = mgh = (6.0 kg) * (9.8 m/s^2) * (9.0 m) = 529.2 J
As the rock falls, its potential energy is converted to kinetic energy, given by the expression (1/2)mv^2, where v is the velocity of the rock. At a height where the kinetic energy of the rock is twice its potential energy, we can write:
(1/2)mv^2 = 2mgh
Simplifying this expression, we get
v^2 = 4gh
At this height, the kinetic energy of the rock is given by:
K = (1/2)mv^2 = (1/2)m(4gh) = 2mgh = 2U
Substituting the values of m, g, and U, we get:
v^2 = 4gh = 4(9.8 m/s^2)h = (2 * 529.2 J) / 6.0 kg = 176 J/kg
Solving for h, we get:
h = (v^2) / (4g) = (176 J/kg) / (4 * 9.8 m/s^2) ≈ 4.5 m
you have been asked to evaluate the ability of a horizontal flow gravity grit chamber to remove particles having a diameter of 1.71 10 4 m. the depth of the grit chamber is 1.0 m. the detention time of the liquid in the grit chamber is 60 s. the particle density is 1.83 g/cm3 . the water temperature is 12 c. assume the density of water is 1,000 kg/m3 .
As the settling distance is less than the chamber depth (1.0 m), the grit chamber can be expected to be effective in removing the particles with the given diameter.Using the Stoke's Law, the settling velocity is calculated as:
What is Stoke's Law ?Stoke's Law is a scientific principle that states that the terminal settling velocity of a small sphere in a viscous fluid is inversely proportional to the fluid's viscosity. It is named after Sir George Gabriel Stokes, who first derived this law in 1851. Stoke's Law is important in many different fields, such as particle sedimentation, particle separation, and fluid mechanics. The law is also used to predict the settling velocity of particles in a fluid, which is important for applications such as filtration.
V = (2 x 9.81 x (1.71 x 10-4)2 x (1.83 - 1)) / (18 x 10-6 x (1 - 0.01))
= 1.39 x 10-4 m/s
The settling distance is calculated as:
S = V x T
= 1.39 x 10-4 x 60
= 0.00834 m
As the settling distance is less than the chamber depth (1.0 m), the grit chamber can be expected to be effective in removing the particles with the given diameter.
To learn more about Stoke's Law
https://brainly.com/question/29565708
#SPJ1
Please help (50 points)
The mass of the Salamander is 0.09 Kg
What is the momentum?Momentum is a physical quantity that describes the motion of an object. It is defined as the product of an object's mass and its velocity. Mathematically, momentum (p) can be expressed as:
p = mv
where m is the mass of the object and v is its velocity.
We know that;
Momentum before collision = Momentum after collision
(5 * 3.6) - (M * 2.2) = (5 + M) * 3.5
Let the mass of the Salamander
18 - 2.2M = 17.5 + 3.5 M
18 - 17.5 = 3.5 M + 2.2 M
M = 0.09 Kg
Learn more about momentum:https://brainly.com/question/30677308
#SPJ1
Please help me find the final answer for this vectors problem!!
The magnitude of the sum of the vectors is 58.3 N.
What is resultant of the two vectors?The resultant of the two vectors is calculated by resolving the vectors as follows;
The sum of the x - component of the vectors is calculated as follows;
Vx = V cos (θ)
where;
V is the magnitude of the vectorVx is the x component of the vectorθ is the inclination of the vector above the horizontalVx = 30 cos (45) + 50 cos (45)
Vx = 56.57 N
The sum of the y - component of the vectors is calculated as follows;
Vy = 30 sin (45) - 50 sin (45)
Vy = -14.14 N
The magnitude of the sum of the vectors;
V = √ (56.56² + (-14.14²)
V = 58.3 N
Learn more about resultant of vectors here: https://brainly.com/question/28047791
#SPJ1
A 10-newton force is required to hold a stretched spring 0. 20 meter from its rest position. What is the potential energy stored in the stretched spring?.
The potential energy stored in stretched spring is 1 Joule with the given data.
The force required to hold a spring in stretched spring is 10 N
As we are to calculate potential energy,
Force = [tex]k * x[/tex]= 10 N
Displacement is x = 0.20 m
Potential Energy can be mathematically defined as:
Ep =[tex](F * x)/2[/tex]
If we place values given in question in the above equation:
Ep =[tex](10*0*20)/2[/tex]
Ep = 2/2
Ep = 1 Joule
Therefore, potential energy stored in stretched spring turns out to be 1 Joule based on the data that we have.
Learn more about potential energy here:
https://brainly.com/question/12807194
#SPJ4
13 A string of length 1.25m fixed at both ends resonates at a maximum frequency of 800Hz. Find the velocity of sound in air.
To solve for the velocity of sound in air, we can use the formula:
v = fλ
where:
v = velocity of sound
f = frequency of the wave
λ = wavelength of the wave
In this problem, we are given the frequency and the length of the string, but we need to find the wavelength. For a string fixed at both ends, the wavelength is given by:
λ = 2L/n
where:
L = length of the string
n = harmonic number
In this case, the string is fixed at both ends, so the harmonic number will be an odd number:
n = 1, 3, 5, ...
We are given that the maximum frequency is 800 Hz, which corresponds to the fundamental frequency (n = 1). Therefore:
λ = 2L/n = 2(1.25 m)/1 = 2.5 m
Now we can substitute the values into the formula for the velocity of sound:
v = fλ = (800 Hz)(2.5 m) = 2000 m/s
Therefore, the velocity of sound in air is 2000 m/s.
Turnbuckle T1 is tightened to a tension of 180 lb and turnbuckle T2 is tightened to 120 lb. Determine the components of the corresponding force and moment reactions at the built-in support at O. Neglect the weight of the structure. 32" 24" A 24" T1 36" 18"
The components of the corresponding force and moment reactions at the built-in support at O are:
Horizontal reaction force = 0 lb
Vertical reaction force = 138.6 lb
Moment reaction = -5370.6 lb-in.
What is Moment Reaction?
In mechanics, a moment reaction refers to the force that acts on an object in response to a moment or torque applied to it. The moment reaction can be thought of as the force that resists the rotation of an object around a given axis. In engineering and physics, moment reactions are important in the analysis of structures and systems that involve rotational motion, such as beams, gears, and engines. They are typically represented as vectors, and can be calculated using mathematical formulas and equations based on the principles of mechanics and Newton's laws of motion.
We can apply the equations of equilibrium to point O to determine the components of the corresponding force and moment reactions. The equations of equilibrium are:
ΣFx = 0 (the sum of forces in the x-direction is zero)
ΣFy = 0 (the sum of forces in the y-direction is zero)
ΣM = 0 (the sum of moments about any point is zero)
Taking the x- and y-axes to be along the horizontal and vertical members, respectively, we have:
ΣFx = -T1 cos(45) - T2 cos(45) = 0
ΣFy = T1 sin(45) + T2 sin(45) = R
ΣM = -T1 cos(45) (24/2) - T2 cos(45) (24 + 36) + R (32) = 0
where R is the reaction force at point O.
Solving these equations, we get:
T1 = 180 lb
T2 = 120 lb
R = 138.6 lb
To find the moment reaction at point O, we can take moments about point O:
ΣM = -T1 cos(45) (24/2) - T2 cos(45) (24 + 36) + R (32) = M
where M is the moment reaction at point O.
Solving this equation, we get:
M = -5370.6 lb-in
Therefore, the components of the corresponding force and moment reactions at the built-in support at O are:
Horizontal reaction force = 0 lb
Vertical reaction force = 138.6 lb
Moment reaction = -5370.6 lb-in.
Learn more about Moment Reaction from given link
https://brainly.com/question/6278006
#SPJ1
The force reaction at the built-in support at O is the sum of the forces from turnbuckles T1 and T2, which can be calculated as follows:
What is force?Force is a push or pull on an object that results from an interaction between two objects. Forces can cause objects to accelerate, decelerate, start moving, stop moving, or change direction. Every interaction in the universe is a result of forces between two objects. Force can be a result of gravity, electromagnetism, or even nuclear forces. Forces are measured in Newtons and can be calculated using the equation F=ma, where F is the force, m is the mass of the object, and a is the object’s acceleration. Force is an integral part of many physical phenomena, and understanding how forces interact is essential to understanding our universe.
Force reaction from T1 = 180 lb
Force reaction from T2 = 120 lb
Total force reaction at O = 180 lb + 120 lb = 300 lb
The moment reaction at the built-in support at O is the sum of the
moments from turnbuckles T1 and T2, which can be calculated as follows:
Moment reaction from T1 = 180 lb x 24 in = 4320 lb-in
Moment reaction from T2 = 120 lb x 18 in = 2160 lb-in
Total moment reaction at O = 4320 lb-in + 2160 lb-in = 6480 lb-in
To learn more about force
https://brainly.com/question/25239010
#SPJ1
