An 81 kg baseball player slides into second base. The coefficiant of kintetic 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 at 1.6 s, what was his intial velocity?
frictionforce= weight*mu= mg*mu
vf=vi-at
solve for vi. Remember F=ma, so a=F/m
To solve this problem, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration (F = m * a). We can calculate the magnitude of the frictional force using this formula.
a) To find the magnitude of the frictional force, we need to determine the acceleration of the player. The coefficient of kinetic friction (µ) relates to the frictional force (Fk) as µ = Fk / Fn, where Fn is the normal force. The normal force is equal to the weight of the player, which is given by the equation Fn = m * g, where m is the mass and g is the acceleration due to gravity (9.8 m/s^2).
First, calculate the normal force:
Fn = m * g
Fn = 81 kg * 9.8 m/s^2
Fn ≈ 794.4 N
Next, calculate the frictional force:
µ = Fk / Fn
0.49 = Fk / 794.4 N
Cross-multiply to solve for Fk:
Fk = 0.49 * 794.4 N
Fk ≈ 389.56 N
Therefore, the magnitude of the frictional force is approximately 389.56 N.
b) To find the player's initial velocity, we can use the equation of motion: vf = vi + a * t, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time taken.
In this case, the player comes to rest, so the final velocity (vf) is 0 m/s. We can rearrange the equation to solve for the initial velocity:
vf = vi + a * t
0 = vi + a * t
vi = -a * t
From the previous part, we calculated the frictional force (Fk) as 389.56 N, which is equal to the product of mass (m) and acceleration (a). So we have:
Fk = m * a
389.56 N = 81 kg * a
Solve for a:
a ≈ 4.81 m/s^2
Given that the time taken (t) is 1.6 seconds, we plug these values into the equation to find the initial velocity:
vi = -a * t
vi = -4.81 m/s^2 * 1.6 s
vi = -7.696 m/s (rounded to three decimal places)
Therefore, the player's initial velocity was approximately -7.696 m/s. The negative sign indicates that the player was moving in the opposite direction of the frictional force.