A 62.0-kg baseball player begins sliding 3.40 m from third base w/ speed of 4.35 m/s. If the player comes to rest at third base (a) how much work was done on the player by friction? (b) what was the coefficient of kinetic friction between the player and the ground?
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To find the work done by friction, you can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
(a) To calculate the work done by friction, we need to find the initial and final kinetic energies of the player.
Given information:
- Mass of the baseball player (m) = 62.0 kg
- Initial speed (v_initial) = 4.35 m/s
- Distance (d) traveled by the player = 3.40 m
- The player comes to rest, so the final speed (v_final) is 0 m/s
To find the initial kinetic energy (KE_initial), we use the formula:
KE_initial = (1/2) * m * v_initial^2
Substituting the values, we have:
KE_initial = (1/2) * 62.0 kg * (4.35 m/s)^2
Next, we calculate the final kinetic energy (KE_final), which is 0, as the player comes to rest:
KE_final = 0 J
The work done by friction (W_friction) can be calculated as the difference between the initial and final kinetic energies:
W_friction = KE_final - KE_initial
(b) To find the coefficient of kinetic friction (μ_k), we can use the equation:
W_friction = μ_k * m * g * d
Where:
- m is the mass of the player,
- g is the acceleration due to gravity (approximately 9.8 m/s^2),
- d is the distance traveled by the player.
From equation (a), we already have the value for W_friction. We can rearrange the equation to solve for μ_k:
μ_k = (W_friction) / (m * g * d)
Substituting the known values, we can calculate the coefficient of kinetic friction (μ_k) between the player and the ground.