A ball with a mass of .2 kg travelling at a speed of 26 m/s is struck by a bat. If the duration of the impulse is .001 seconds and the speed of the ball afterwards is the same as before, what is the average force (to the nearest Newton) of the impact?
On the other hand, if the magnitude of the average force in the problem above is 20000 N, what is the speed to the nearest m/s after collision?
(Average force)* (Impact duration)=
(change in momentum) = 2 M V
Avg. Force = 2*(0.2)*26/0.001 Newtons
Crunch the numbers.
For the second part, solve for the change in momentum. Add it to the initial momentum (which is backwards and negative) to get the final momentum, and from that get the speed.
To find the average force of the impact, we can use the principle of impulse and momentum. Impulse is the change in momentum of an object and can be calculated by multiplying the force applied to an object by the duration of the force.
First, we need to calculate the initial momentum of the ball. Momentum is defined as the product of mass and velocity. Therefore, the initial momentum of the ball is:
Initial momentum = mass × initial velocity
Initial momentum = 0.2 kg × 26 m/s
Initial momentum = 5.2 kg⋅m/s
Since the final speed of the ball after the impact is the same as before, the final momentum remains the same:
Final momentum = 5.2 kg⋅m/s
To calculate impulse, we can subtract the initial momentum from the final momentum:
Impulse = Final momentum - Initial momentum
Impulse = 5.2 kg⋅m/s - 5.2 kg⋅m/s
Impulse = 0 kg⋅m/s
The impulse is 0 kg⋅m/s, which implies that the net force acting on the ball during the impact is also 0 N. However, the problem states that the duration of the impulse is 0.001 seconds. Since impulse is equal to the force multiplied by the duration, we can rearrange the equation to solve for force:
Force = Impulse / duration
Force = 0 kg⋅m/s / 0.001 s
Force = 0 N / 0.001 s
Force = 0 N
Therefore, the average force of the impact is 0 Newtons.