Hello,
I don't know how about to answering this question:
work out the problem of a ball of mass m that falls a distance h from rest. It hits the floor and rebounds to its starting height. (a) What total time ie required for the motion? (Neglect the time of contact with the floor.) (b) What is the speed of the ball as it strikes the floor? (c) What is the change in momentum of the ball as it strikes the floor and rebounces? (d) Calculate the average force that the ball exerts on the floor averaged over the whole time interval of part (a). Is this surprising?
Is there like a formula in particular that I should be looking at?
The return bounce takes as long as it takes to fall, so find the time of fall and double it.
h=1/2 g t^2 solve for time.
speed= g * time
change of momentum= 2* momentumat floor
= 2*m*speed
The force of the ball is gravitational pull, which is mg. That is the force on the ball, and it is the force on the Earth.
You can get the force also by doing change of momentum/totaltimefalling.
Neat. This doesn't surprise me, gravity is gravity.
To solve this problem, you can use the following formulas and steps:
(a) First, you need to find the time it takes for the ball to fall from rest to the floor and then rebound back to its starting height. Since the return bounce takes as long as the fall, you can find the time of fall and double it.
1. Use the formula for the height of free fall: h = (1/2)gt^2, where h is the distance, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time of fall.
2. Rearrange the formula to solve for time: t = √(2h/g).
(b) To find the speed of the ball as it strikes the floor, you can use the formula for speed:
1. Use the formula for speed: speed = g * time, where speed is the velocity, g is the acceleration due to gravity, and time is the time of fall.
(c) The change in momentum of the ball as it strikes the floor and rebounds can be calculated using the formula:
1. Use the formula for momentum: momentum = mass * velocity.
2. Since the ball rebounds to its starting height, the change in momentum is equal to 2 times the momentum at the floor.
(d) To calculate the average force that the ball exerts on the floor averaged over the whole time interval of part (a), you can use the formula:
1. Use the formula for force: force = change in momentum / total time falling.
It is not surprising that the average force exerted by the ball on the floor is equal to its weight (mg). This is because gravity is always acting on the ball, and the force on the ball is equal in magnitude and opposite in direction to the force on the Earth.