A .5 kg football is thrown and reaches a stationary receiver with a speed of 15m/s. The receiver catches the ball and brings it to rest in .2 sec.
a) What is the impulse delivered to the ball?
b) What is the average force exerted on the receiver?
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To solve this problem, we need to use the concepts of impulse and average force.
a) Impulse is given by the equation:
Impulse = Change in momentum
The momentum of an object is the product of its mass and velocity:
Momentum = mass × velocity
Given that the football has a mass of 0.5 kg and reaches the receiver with a speed of 15 m/s, we can calculate its initial momentum:
Initial momentum = 0.5 kg × 15 m/s = 7.5 kg·m/s
Since the receiver brings the ball to rest, its final momentum is zero:
Final momentum = 0 kg·m/s
Therefore, the change in momentum is:
Change in momentum = Final momentum - Initial momentum
= 0 - 7.5 kg·m/s
= -7.5 kg·m/s
The impulse delivered to the ball is equal to the change in momentum:
Impulse = -7.5 kg·m/s
b) The average force exerted on the receiver can be calculated by using the equation:
Impulse = Average force × Time
We already know the impulse delivered to the ball (-7.5 kg·m/s) and the time taken to bring the ball to rest (0.2 s). Plugging these values into the equation above, we can solve for the average force:
-7.5 kg·m/s = Average force × 0.2 s
Simplifying the equation gives:
Average force = -7.5 kg·m/s / 0.2 s
= -37.5 N
The negative sign indicates that the force is exerted in the opposite direction of motion (to bring the ball to rest).
Therefore, the average force exerted on the receiver is -37.5 N.