A 103-kg baseball player slides into second base. The coefficient of kinetic friction between the player and the ground is ìk = 0.729. (a) What is the magnitude of the frictional force? (b) If the player comes to rest after 1.27 s, what is his initial speed?
weight = 103 (big guy!) * 9.81 = 1010 N
F = .729 * 1010 = 737 N
F = m a
-737 = 103 a
(negative because stopping)
a = - 7.15
v = Vi + a t
0 = Vi -7.15 (1.27)
Vi = 9.08 m/s
To find the magnitude of the frictional force, we can use the formula:
Frictional force = coefficient of kinetic friction * normal force
(a) The normal force acting on the player is equal to the player's weight, which can be calculated using the formula:
Weight = mass * acceleration due to gravity
Given that the player's mass is 103 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we have:
Weight = 103 kg * 9.8 m/s^2
Now, substitute this value into the formula for the frictional force:
Frictional force = 0.729 * (103 kg * 9.8 m/s^2)
Calculating the above expression will give you the magnitude of the frictional force.
(b) To find the player's initial speed, we can use the relationship between acceleration, time, and initial velocity:
Final velocity = initial velocity + (acceleration * time)
In this case, the player comes to rest after 1.27 s, so the final velocity is 0 m/s. The acceleration can be calculated using the formula:
Acceleration = frictional force / mass
Substitute the known values into the formula to calculate the acceleration.
Finally, use the above formulas to find the initial velocity by rearranging the equation:
Initial velocity = (Final velocity - (Acceleration * time))
Substitute the values of the final velocity, acceleration, and time to find the initial speed of the player.