A 69-kg base runner begins his slide into second base when he is moving at a speed of 3.7 m/s. The coefficient of friction between his clothes and Earth is 0.70. He slides so that his speed is zero just as he reaches the base.
(a) How much mechanical energy is lost due to friction acting on the runner?
(b) How far does he slide?
To find the answers to the given question, we need to use the concepts of work, energy, and friction. Here are the steps to solve this problem:
(a) To find the mechanical energy lost due to friction, we need to calculate the work done by friction on the runner.
1. Determine the initial kinetic energy (KE_initial) of the runner using the formula:
KE_initial = 0.5 * mass * velocity^2
Plugging in the values:
KE_initial = 0.5 * 69 kg * (3.7 m/s)^2
2. Determine the final kinetic energy (KE_final) of the runner. Since the runner's speed is zero at the end, KE_final is zero.
3. The work done by friction is given by the formula:
Work = KE_initial - KE_final
Plugging in the values:
Work = 0.5 * 69 kg * (3.7 m/s)^2 - 0
Calculate the value of Work to find the mechanical energy lost due to friction.
(b) To find the distance the runner slides, we can use the work-energy principle in conjunction with the concept of work done by friction.
1. The work done by friction is equal to the change in mechanical energy. We already calculated this value in step (a) as the mechanical energy lost due to friction.
2. The work done by friction is also given by the formula:
Work = force of friction * distance
Using this equation, we can rearrange it to solve for distance:
Distance = Work / force of friction
Since we already know the value of Work from step (a), we need to determine the force of friction.
3. The force of friction can be found using the formula:
Force of friction = coefficient of friction * normal force
The normal force is equal to the weight of the runner, which is given by:
Normal force = mass * gravitational acceleration
Plugging in the values, we can calculate the force of friction.
4. Finally, we can use the calculated values of Work and force of friction to find the distance the runner slides by dividing Work by the force of friction.
Following these steps, we can find the answers to both parts (a) and (b) of the question.