A racket exerted an average force of 152.0 N on a ball initially at rest. If the ball has a mass of 0.070 kg and was in contact with the racket for 0.030 s, what was the kinetic energy of the ball as it left the racket?
a = F/M = 152/0.07 = 2171 m/s^2
V = Vo + a*t
Vo = 0
a = 2171 m/s^2
t = 0.030 s.
V = ?
KE = o.5*M*V^2
Thank you so much Henry!
Glad I could help!
KE= 1/2 mv^2
= 1/2 (0.070 kg) v^2 ; Ft= mv
v= Ft/m
v=(152N)(0.030s)/0.070kg
V= 65 m/s
= 1/2 ((0.070 kg) (65 m/s) ^2
= 148.5 J
Well, let me calculate that for you. To find the kinetic energy of the ball, we can use the formula:
Kinetic Energy = (1/2) * mass * velocity^2
Now, to find the velocity of the ball, we need to know the acceleration it experienced while in contact with the racket. Can you provide that information? Otherwise, I'll have to resort to some clownish estimations!
To find the kinetic energy of the ball as it left the racket, we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.
The work done on the ball can be calculated using the formula:
Work = Force x Distance
However, in this case, we don't have the distance. But we can use the average force, mass, and time to find the distance traveled by the ball.
First, calculate the acceleration of the ball using Newton's second law:
Force = mass x acceleration
Rearranging this equation, we can find the acceleration:
acceleration = Force / mass
Substitute the given values:
acceleration = 152.0 N / 0.070 kg
Next, use the kinematic equation to find the distance traveled by the ball:
distance = (1/2) x acceleration x time^2
Substitute the known values:
distance = (1/2) x acceleration x (0.030 s)^2
Once we have the distance, we can calculate the work done on the ball:
Work = Force x Distance
Finally, we can use the work-energy theorem to find the change in kinetic energy of the ball. Since the ball is initially at rest, the initial kinetic energy is 0. Therefore, the change in kinetic energy is equal to the work done:
Change in kinetic energy = Work
The kinetic energy of the ball as it left the racket is equal to the change in kinetic energy.