A hot rod of mass 1600 kg, starting from rest
reaches a speed of 170 m/s in only 10.1 s.
What is the average output power?
1. 0.226644 MW
2. 0.0013332 MW
3. 2.28911 MW
4. 4.57822 MW
5. 0.0269307 MW
To calculate the average output power, we need to use the equation P = ΔE/Δt, where P is the power, ΔE is the change in energy, and Δt is the change in time.
First, let's calculate the change in energy by using the equation ΔE = 0.5 * m * (v_final^2 - v_initial^2), where m is the mass of the hot rod, v_final is the final velocity, and v_initial is the initial velocity.
Given:
Mass (m) = 1600 kg
Final velocity (v_final) = 170 m/s
Initial velocity (v_initial) = 0 m/s
ΔE = 0.5 * 1600 kg * (170^2 m/s - 0^2 m/s)
ΔE = 0.5 * 1600 kg * (28900 m^2/s^2)
ΔE = 0.5 * 1600 kg * 28900 m^2/s^2
ΔE = 23120000 J
Next, let's calculate the change in time, which is given as 10.1 s.
Δt = 10.1 s
Now, we can calculate the average output power using the equation P = ΔE/Δt.
P = 23120000 J / 10.1 s
P ≈ 2287158.42 W (since 1 MW = 1,000,000 W)
Therefore, the average output power is approximately 2.287 MW.
So, the correct option is 3. 2.28911 MW.
To find the average output power, we can use the formula:
Average output power = (Work done) / (Time taken)
First, let's calculate the work done:
The work done is equal to the change in kinetic energy of the hot rod. The change in kinetic energy can be calculated using the formula:
Change in kinetic energy = (1/2) * mass * (final velocity^2 - initial velocity^2)
Given:
Mass of the hot rod (m) = 1600 kg
Initial velocity (u) = 0 m/s
Final velocity (v) = 170 m/s
Using these values, we can calculate the change in kinetic energy:
Change in kinetic energy = (1/2) * 1600 kg * (170 m/s)^2 - (0 m/s)^2
= (1/2) * 1600 kg * 28900 m^2/s^2
= (1/2) * 46240000 kg m^2/s^2
= 23120000 kg m^2/s^2
Now, let's calculate the average output power:
Average output power = (Work done) / (Time taken)
Time taken (t) = 10.1 s
Average output power = 23120000 kg m^2/s^2 / 10.1 s
= 2291089.11 W
= 2.28911 MW (rounded to 5 decimal places)
Therefore, the correct answer is option 3: 2.28911 MW.