You are hitting a tennis ball against a wall. The 0.057-kg tennis ball traveling at 29 m/s strikes the wall and rebounds at the same speed. Earth is the object of reference.
Determine the ball's change in momentum (magnitude).
so the magnitude is 3.31 kg m/s
-29 m/s - (+29 m/s) = -58 m/s velocity change
change in momentum = -.057(58) kg m/s
Well, if the ball is hitting against a wall with the same speed, we can't really say it has changed its momentum. It's more like a love-hate relationship between the ball and the wall - they just keep bouncing the same way, without any change. So, the change in momentum of the ball would be zero, just like my chances of winning a tennis match against Roger Federer.
To determine the ball's change in momentum, we need to calculate the initial momentum and the final momentum, and then find the difference between them.
The momentum of an object is given by the product of its mass and velocity. In this case, the tennis ball has a mass of 0.057 kg and a velocity of 29 m/s.
The initial momentum can be calculated as:
Initial momentum = mass * initial velocity
Initial momentum = 0.057 kg * 29 m/s
Calculating that gives us:
Initial momentum = 1.653 kg·m/s
Since the ball rebounds at the same speed, its final velocity is also 29 m/s. So the final momentum can be calculated as:
Final momentum = mass * final velocity
Final momentum = 0.057 kg * 29 m/s
Calculating that gives us:
Final momentum = 1.653 kg·m/s
Finally, to find the change in momentum, we simply subtract the initial momentum from the final momentum:
Change in momentum = Final momentum - Initial momentum
Change in momentum = 1.653 kg·m/s - 1.653 kg·m/s
Calculating that gives us:
Change in momentum = 0 kg·m/s
Therefore, the magnitude of the ball's change in momentum is 0 kg·m/s.