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A crane lifts a package with a mass of 95.5 kg. If the power output of the crane is 112 watts, at what speed can the package be lifted, in m/s?

Answer :

Final answer:

To find the speed at which a 95.5 kg package can be lifted with a crane power output of 112 watts, use the power formula Power = Force x Velocity. The force here is the weight of the package (mass x gravity). Solving for velocity, you get approximately 0.12 m/s.

Explanation:

The student's question asks: at what speed can a package of mass 95.5 kg be lifted if the power output of the crane is 112 watts? To answer this, we need to apply the formula for power in terms of force and velocity: Power = Force × Velocity. The force exerted by the crane is equal to the weight of the package, which is the mass of the package times the acceleration due to gravity (g = 9.8 m/s2).

First, calculate the force (weight):
Force = Mass × Gravity
Force = 95.5 kg × 9.8 m/s2
Force = 935.9 N

Next, rearrange the power formula to solve for velocity:
Velocity = Power / Force
Velocity = 112 W / 935.9 N
Velocity ≈ 0.12 m/s

Therefore, the package can be lifted at a speed of approximately 0.12 m/s by the crane with a power output of 112 watts.

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