A) 6.64 m/s downward
B) 0.026 s
C) -40.9 N
Explanation:
A)
We can solve this problem by using the law of conservation of energy.
In fact, since the total mechanical energy of the ball must be conserved, this means that the initial gravitational potential energy of the ball before the fall is entirely converted into kinetic energy just before it reaches the floor.
So we can write:
where
m = 0.160 kg is the mass of the ball
is the acceleration due to gravity
h = 2.25 m is the initial height of the ball
v is the final velocity of the ball before hitting the ground
Solving for v, we find:
And the direction of the velocity is downward.
B)
The motion of the ballduring the collision is a uniformly accelerated motion (= with constant acceleration), so the time of impact can be found by using a suvat equation:
where:
v is the final velocity
u is the initial velocity
s is the displacement of the ball during the impact
t is the time
Here we have:
u = 6.64 m/s is the velocity of the ball before the impact
v = 0 m/s is the final velocity after the impact (assuming it comes to a stop)
s = 0.087 m is the displacement, as the ball compresses by 0.087 m
Therefore, the time of the impact is:
C)
The force exerted by the floor on the ball can be found using the equation:
where
is the change in momentum of the ball
t is the time of the impact
The change in momentum can be written as
So the equation can be rewritten as
Here we have:
m = 0.160 kg is the mass of the ball
v = 0 is the final velocity
u = 6.64 m/s is the initial velocity
t = 0.026 s is the time of impact
Substituting, we find the force:
And the sign indicates that the direction of the force is opposite to the direction of motion of the ball.