a tennis player swings her 1000g racket with a speed of 6.00 m/s. she hits a 60g tennis ball that was approaching her at a speed of 18.0 m/s . the ball rebounds at 43.0 m/s. a)how fast is her racket moving immediately after the impact? you can ignor the interaction of the racket with her hand for the brief duration of the collision. b) if the tennis ball and racket are in contact for 10.0 m, whAT IS THE AVEREGE force that the racket exerts on the ball?
1.the unit in which force is measured
2. It changes both the direction and the speed of the ball
3. the force will cause a change in the momentum of the object
4. The state of motion of an object with mass
a) Apply conservation of momentum to the ball-racket impact.
b) Your units for the contact time (meters) do not make sense. Did you mean milliseconds?
Anyway, use (ball's momentum change) = impulse
= force * time
6.4
To solve this question, we can use the principle of conservation of momentum.
a) To find the speed of the racket immediately after the impact, we can use the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.
The equation for momentum is given by:
momentum = mass x velocity
The total momentum before the collision can be calculated as the sum of the momentum of the racket and the momentum of the ball:
Total momentum before = (Mass of racket x velocity of racket) + (Mass of ball x velocity of ball)
Given:
Mass of racket = 1000g = 1kg (since 1kg = 1000g)
Velocity of racket = 6.00 m/s
Mass of ball = 60g = 0.06kg (since 1kg = 1000g)
Velocity of ball = 18.0 m/s
Substituting these values into our equation, we get:
Total momentum before = (1kg x 6.00 m/s) + (0.06kg x 18.0 m/s)
Now, to find the speed of the racket immediately after the impact, we can use the principle of conservation of momentum.
Total momentum after the collision = (Mass of racket + Mass of ball) x velocity of racket after collision
Given:
Velocity of ball after collision = 43.0 m/s
Substituting these values into our equation, we get:
Total momentum after = (1kg + 0.06kg) x velocity of racket after collision
Since the total momentum before the collision is equal to the total momentum after the collision, we can set the two equations equal to each other:
(1kg x 6.00 m/s) + (0.06kg x 18.0 m/s) = (1kg + 0.06kg) x velocity of racket after collision
Now we can solve for the velocity of the racket after the collision:
(6.00 + 1.08) kg.m/s = (1.06kg) x velocity of racket after collision
7.08 kg.m/s = 1.06 kg x velocity of racket after collision
Dividing both sides of the equation by 1.06 kg, we find:
velocity of racket after collision = 7.08 kg.m/s / 1.06 kg
Therefore, the speed of the racket immediately after the impact is approximately 6.67 m/s.
b) To find the average force that the racket exerts on the ball, we can use the equation:
Force = change in momentum / time
Given:
Change in momentum = (Mass of ball x velocity of ball after collision) - (Mass of ball x velocity of ball before collision)
Time = 10.0 m
Substituting the given values into the equation, we get:
Force = (0.06kg x 43.0 m/s) - (0.06kg x 18.0 m/s) / 10.0 m
Now we can calculate the average force:
Force = (2.58 kg.m/s - 1.08 kg.m/s) / 10.0 m
Force = 1.5 kg.m/s / 10.0 m
Therefore, the average force that the racket exerts on the ball is approximately 0.15 N.