(ii) a cord of mass 0.55 kg is stretched°between two supports 30 in apart. if the tension in the cord· is 150n, how long will it take a pulse to travel from one support to the other?

Answers

Answer 1

It will take approximately 0.053 seconds for a pulse to travel from one support to the other if a cord of mass 0.55 kg is stretched° between two supports 30 in apart and if the tension in the cord· is 150n

We'll be using the following terms in the solution: mass, tension, distance, pulse, and time. Calculate the linear mass density (μ) of the cord.
μ = (mass of the cord) / (length of the cord)
μ = 0.55 kg / 30 in

Note: We need to convert inches to meters. There are 0.0254 meters in 1 inch.
30 in * 0.0254 m/in = 0.762 m

Now, we can find the linear mass density:
μ = 0.55 kg / 0.762 m = 0.721 kg/m

Calculate the speed (v) of the pulse on the cord using tension (T) and linear mass density (μ).
v = √(T / μ)
v = √(150 N / 0.721 kg/m)

Solve for the speed of the pulse.
v ≈ √(207.49 m²/s²) ≈ 14.4 m/s

Calculate the time (t) it takes for the pulse to travel between the supports.
t = (distance between supports) / (speed of pulse)
t = 0.762 m / 14.4 m/s

Solve for the time.
t ≈ 0.053 s

So, it will take approximately 0.053 seconds for a pulse to travel from one support to the other.

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Related Questions

a potw is being designed to treat 2.5 mgd. size the grit chamber (calcu- late the volume—do not specify dimensions).

Answers

The volume of a POTW is being designed to treat 2.5 MGD is 2,600 gallons.

To size the grit chamber for a POTW (Publicly Owned Treatment Works) being designed to treat 2.5 MGD (million gallons per day), we need to calculate the volume. The volume of a grit chamber can be determined using the formula:

Volume = Flow Rate (MGD) × Detention Time × Conversion Factor

Detention time for grit chambers is typically between 1 to 2 minutes. Let's use a detention time of 1.5 minutes for this calculation. We also need to convert the flow rate from MGD to gallons per minute (GPM) and the detention time from minutes to days. There are 1,440 minutes in a day and 1,000,000 gallons in a MGD.

Conversion Factor: 1 MGD = 1,000,000 gallons and 1 day = 1,440 minutesFlow Rate in GPM: 2.5 MGD × (1,000,000 gallons / 1 MGD) × (1 day / 1,440 minutes) = 1,736.11 GPMDetention Time in days: 1.5 minutes × (1 day / 1,440 minutes) = 0.00104 days

Now, we can calculate the volume:

Volume = 1,736.11 GPM × 0.00104 days × 1,440 minutes / 1 day

Volume ≈ 2,600 gallons

Therefore, the volume of the grit chamber for a POTW designed to treat 2.5 MGD should be approximately 2,600 gallons.

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