A man lifts a 3 kg crate from the floor to a shelf (2 m high) at constant speed*.
What was the change in KE of the crate?
What is the change in the PE of the crate?
If it takes 2 s for the man to lift the crate to the shelf, find the man's power output.
The energy (work) required to life any mass against a graviatational force is force*distance or mgh. This translates to a change of PE.
Power=work/time.
I will be happy to check your thinking.
To answer these questions, we need to understand the concepts of kinetic energy, potential energy, and power.
1. Change in kinetic energy (ΔKE):
The crate is lifted at a constant speed, which means its kinetic energy remains constant. Therefore, the change in kinetic energy is zero (0).
2. Change in potential energy (ΔPE):
The potential energy of an object depends on its height and mass. The formula for potential energy is PE = mgh, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s² on Earth), and h is the height.
In this case, the crate is lifted to a height of 2 m. The mass of the crate is given as 3 kg. Substituting these values into the formula, we get:
ΔPE = (mgh₂) - (mgh₁)
= mg(h₂ - h₁)
= 3 kg * 9.8 m/s² * (2 m - 0 m)
= 58.8 Joules
Therefore, the change in potential energy of the crate is 58.8 Joules.
3. Power output of the man (P):
Power is the rate at which work is done. In this case, the work done by the man is equal to the change in potential energy, since the kinetic energy doesn't change. The formula for power is P = W/t, where W is the work done and t is the time taken.
We have already calculated the change in potential energy as 58.8 Joules. The time taken to lift the crate is given as 2 seconds. Substituting these values into the formula, we get:
P = 58.8 J / 2 s
= 29.4 Watts
Therefore, the man's power output is 29.4 Watts.