A 95.9-kg baseball player slides into second base. The coefficient of kinetic friction between the player and the ground is ìk = 0.554. (a) What is the magnitude of the frictional force? (b) If the player comes to rest after 1.63 s, what is his initial speed?
Wp = m*g = 95.9kg * 9.8N/kg = 940 N. =
Wt. of player.
a. Fk = 0.554 * 940 = 520.7 N.
b. Fn = m*a
a = Fn/m = (940-521)/95.9 = 4.37m/s^2.
V = Vo + a*t = 0
Vo = -a*t = -(-4.37*1.63) = 7.1 m/s.
To find the magnitude of the frictional force, we can use the formula:
Frictional Force = coefficient of kinetic friction * Normal Force
(a) First, we need to find the Normal Force acting on the baseball player. The Normal Force is the force exerted by a surface to support the weight of an object resting on it. It is equal in magnitude but opposite in direction to the force of gravity acting on the object.
The force of gravity can be calculated using the formula:
Force of gravity = mass * acceleration due to gravity
In this case, the player's mass is 95.9 kg, and the acceleration due to gravity is 9.8 m/s². So, the force of gravity on the player is:
Force of gravity = 95.9 kg * 9.8 m/s²
Next, we can calculate the Normal Force using the fact that the player is on a horizontal surface, and there is no vertical acceleration. So, the Normal Force and the force of gravity are equal in magnitude.
Normal Force = Force of gravity = 95.9 kg * 9.8 m/s²
Now, we can find the magnitude of the frictional force by multiplying the coefficient of kinetic friction by the Normal Force:
Frictional Force = 0.554 * Normal Force
Substituting the value of the Normal Force, we get:
Frictional Force = 0.554 * (95.9 kg * 9.8 m/s²)
Calculate the value to find the magnitude of the frictional force.
(b) To find the player's initial speed, we can use the equation of motion:
Final Velocity = Initial Velocity + (Acceleration * Time)
Since the player comes to rest after sliding, the final velocity is 0 m/s. The acceleration can be determined using Newton's second law:
Force = mass * acceleration
The only horizontal force acting on the player is the frictional force, so we can use:
Frictional Force = mass * acceleration
Solving for acceleration, we get:
Acceleration = Frictional Force / mass
Now, we can substitute the values of the frictional force and mass into the equation to find acceleration. Once we have acceleration, we can use the equation of motion to find the initial speed.
Initial Velocity = Final Velocity - (Acceleration * Time)
Substituting the values of final velocity, acceleration, and time, you can calculate the initial speed of the player.