An 81 kg baseball player slides into second base. The coefficient of kinetic friction between the player and the ground is .49.
a) what is the magnitude of the frictional force?
b) If the player comes to a rest after 1/6s, what was his initial velocity?
To solve this problem, we can use Newton's Laws of Motion. The first step is to find the magnitude of the frictional force.
a) Magnitude of the frictional force:
The frictional force can be calculated using the equation:
frictional force = coefficient of friction * normal force
The normal force can be calculated using the equation:
normal force = mass * acceleration due to gravity
In this case, the mass of the baseball player is 81 kg. The acceleration due to gravity is approximately 9.8 m/s^2.
normal force = 81 kg * 9.8 m/s^2 = 794.8 N
Now we can calculate the frictional force:
frictional force = 0.49 * 794.8 N = 389.67 N
Therefore, the magnitude of the frictional force is 389.67 N.
b) Initial velocity:
To find the initial velocity, we can use the equation:
final velocity = initial velocity + (acceleration * time)
In this case, the final velocity is 0 m/s (as the player comes to rest), the time is 1/6 s, and the acceleration can be calculated using the equation:
acceleration = frictional force / mass
acceleration = 389.67 N / 81 kg = 4.810 m/s^2
Now we can rearrange the equation to solve for the initial velocity:
0 m/s = initial velocity + (4.810 m/s^2 * 1/6 s)
Simplifying the equation:
0 m/s = initial velocity + 0.802 m/s
Therefore, the initial velocity is -0.802 m/s.
Note: The negative sign indicates that the initial velocity is in the opposite direction of the final velocity.
To find the answers to these questions, we need to use the formulas related to friction and acceleration.
First, let's find the magnitude of the frictional force (question a) using the formula:
Frictional force = coefficient of kinetic friction * Normal force
The normal force is the force exerted by the surface perpendicular to it. In this case, it is equal to the player's weight, which is the mass multiplied by the acceleration due to gravity (9.8 m/s^2):
Normal force = mass * acceleration due to gravity
Normal force = 81 kg * 9.8 m/s^2
Next, substitute the value of the normal force into the formula for frictional force:
Frictional force = 0.49 * (81 kg * 9.8 m/s^2)
Now, calculate the frictional force.
Frictional force = 0.49 * (794.4 kg*m/s^2)
Frictional force = 389.256 N
Therefore, the magnitude of the frictional force is 389.256 N.
Moving on to question b, we have the player coming to a stop after a certain time interval (1/6 second). We can use the formula for acceleration:
Acceleration = (final velocity - initial velocity) / time
Since the player comes to a stop, the final velocity is zero. Rearranging the formula, we can solve for the initial velocity:
Initial velocity = final velocity - (acceleration * time)
Since we know the acceleration due to friction, which acts in the opposite direction of motion, we can substitute the magnitude of the frictional force divided by the player's mass into the formula:
Initial velocity = 0 - ((magnitude of frictional force) / mass * time)
Initial velocity = - (389.256 N) / (81 kg * (1/6 s))
Now, calculate the initial velocity.
Initial velocity = - (389.256 N) / (81 kg * (1/6 s))
Initial velocity = - (389.256 N) / (13.5 kg/s)
Initial velocity = - 28.8346 m/s
Therefore, the player's initial velocity is approximately -28.8346 m/s (the negative sign indicates that the velocity is in the opposite direction of motion).
frictional force=mg*mu
force*time=mass*changevelocity
solve for vi