An 85-kg football player traveling 5.0 m/s is stopped in 1.0 s by a tackler. What average power is required to stop him?

검증된 단계별 안내

Determine the initial kinetic energy of the football player using the formula for kinetic energy:

K_{i} = (1/2)mv

², where

m

is the mass (85 kg) and

v

is the velocity (5.0 m/s).

Since the player is stopped, the final kinetic energy is zero. The change in kinetic energy is equal to the initial kinetic energy:

ΔK = K_{i} - K_{f}

, where

K_{f} = 0

The work done to stop the player is equal to the change in kinetic energy:

W = ΔK

. Substitute the value of

ΔK

from the previous step.

The average power required to stop the player is given by the formula:

P = W / t

, where

t

is the time interval (1.0 s). Substitute the value of

W

from the previous step.

Simplify the expression to find the average power. Ensure all units are consistent (mass in kg, velocity in m/s, time in seconds) to get the power in watts (W).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Momentum

Momentum is the product of an object's mass and its velocity, represented by the equation p = mv. In this scenario, the football player's momentum before being tackled can be calculated using his mass (85 kg) and his speed (5.0 m/s). Understanding momentum is crucial for analyzing the changes in motion and the forces involved in stopping the player.

Impulse

Impulse is defined as the change in momentum of an object when a force is applied over a period of time. It can be calculated using the formula Impulse = Force × Time. In this case, the tackler applies a force over 1.0 second to stop the player, and calculating the impulse will help determine the average force exerted during the tackle.

Power

Power is the rate at which work is done or energy is transferred, expressed as Power = Work / Time. In this context, the work done to stop the football player can be related to the impulse and the time taken (1.0 s). Calculating the average power required to stop the player involves determining the work done in stopping him and dividing it by the time interval.