An 81-kg baseball player slides into second base. The coefficient of kinetic friction between the player and the ground is 0.49. (a) What is the magnitude of the frictional force? (b) If the player comes to rest after 1.6 s, what was his initial velocity?
To find the magnitude of the frictional force, we need to use the equation:
Frictional force = coefficient of kinetic friction * normal force
The normal force is the force exerted by the ground on the baseball player perpendicular to the surface. In this case, it is equal to the player's weight (mg).
(a) To calculate the magnitude of the frictional force:
1. Calculate the normal force:
Normal force = player's weight = mass * gravity
Mass = 81 kg, gravity = 9.8 m/s^2
Normal force = 81 kg * 9.8 m/s^2
2. Calculate the frictional force using the coefficient of kinetic friction:
Frictional force = coefficient of kinetic friction * normal force
Substitute the known values:
Frictional force = 0.49 * (81 kg * 9.8 m/s^2)
Calculate this to get the magnitude of the frictional force.
(b) To find the initial velocity of the player:
1. We know that acceleration is given by the equation:
Acceleration = change in velocity / time
2. In this case, the player comes to rest, so the change in velocity is the final velocity (0 m/s) minus the initial velocity (which we need to find). The time is given as 1.6 seconds.
Rearrange the equation to solve for the initial velocity:
Initial velocity = (final velocity - acceleration * time)
Substitute the known values:
Initial velocity = (0 m/s - acceleration * 1.6 s)
Calculate this to find the initial velocity of the player.