Calculating Force on a Bouncing Ball

In summary, the problem involves finding the average magnitude of the force exerted on a bouncing ball that has a mass of 0.2 kg and initial speed of 5 m/s, rebounds with a speed of 4 m/s, and is in contact with the floor for 1.5 ms. After some initial confusion, the correct methodology involves calculating the change in momentum using the given initial and final velocities, and then using the time of contact (1.5 ms) to solve for the net force. The final answer may seem large, but it is correct given the values provided.
  • #1
fball558
147
0
Force on a bouncing ball?

Homework Statement



this should be easy but for some reason I am making a mistake here is the problem

A ball whose mass is 0.2 kg hits the floor with a speed of 5 m/s and rebounds upward with a speed of 4 m/s. If the ball was in contact with the floor for 1.5 ms (1.5 E -3 s), what was the average magnitude of the force exerted on the ball by the floor?


The attempt at a solution

what i did was use delta(P) = Fnet * delta(t)
change in momentum equals net force times change in time

i can find change of momentum of the ball by

P3 = ((m (+-) M) / (m + M)) * P1
P1 is inital momentum of ball so just m*v .2 * 5 = 1 but would be - because movind down
m is just .2 and big M is mass of Earth
solve equation i got P3 to be 1
so i took final P minus inital P and get 2
then divided this by 1.5 E -3 to find Fnet and get some answer like 1333.333 N
that seems too big so was wondering where i messed up (or is it right)
 
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  • #2


I don't understand your methodology for solving for the momentum. Both the initial and final velocities of the ball are given meaning that both momenta can be calculated directly, right?
 
  • #3


BishopUser said:
I don't understand your methodology for solving for the momentum. Both the initial and final velocities of the ball are given meaning that both momenta can be calculated directly, right?

wow no for some reason i was thinking the given speeds was the acceleration. then i had to use that to figure out velocity and then momentum.

so i would use p = m*v to find final and inital
final = .2 * 4 = .8
inital = .2 * 5 = 1 (which will be -1 because it is moving towards the earth)
final - inital = 1.8 this is my change in momentum

then could i just use the change in momentum = fnet times change in time?
would my change in time just be the time it is in contact with the floor?
 
  • #4


Well, the time given is the time that the ball is in contact with the floor, which is when the momentum change is taking place, so yes I would say that is the correct delta T to plug in.
 
  • #5


BishopUser said:
Well, the time given is the time that the ball is in contact with the floor, which is when the momentum change is taking place, so yes I would say that is the correct delta T to plug in.

oh ok... i got it now.
im sleep deprived and my brain
is not working right now. need to
get more than 3 hrs of sleep tonight
haha
thanks for the help!
 

1. What is the relationship between force and the height of a bouncing ball?

The relationship between force and the height of a bouncing ball is described by the Law of Conservation of Energy. As the ball bounces, it converts potential energy into kinetic energy and back again. The force acting on the ball is responsible for this energy conversion, and the height of the bounce depends on the amount of force applied.

2. How does the surface affect the force on a bouncing ball?

The surface on which a ball bounces can greatly affect the force acting on it. A softer surface, such as a foam mat, will absorb more of the force and result in a lower bounce. A harder surface, like concrete, will reflect more of the force and result in a higher bounce. The type of surface also affects the duration of the force acting on the ball, which can impact the height and speed of the bounce.

3. What role does gravity play in the force on a bouncing ball?

Gravity is a major factor in the force acting on a bouncing ball. The force of gravity pulls the ball towards the ground, and as it falls, the potential energy is converted into kinetic energy. This kinetic energy then causes the ball to bounce back up, with the force of gravity acting against it. The strength of gravity can also affect the height and speed of the bounce.

4. How does the weight of the ball impact the force on a bouncing ball?

The weight of the ball can affect the force acting on it in two ways. First, a heavier ball will have more potential energy when dropped, resulting in a higher bounce. Second, a heavier ball will have more momentum when it hits the ground, resulting in a stronger force pushing it back up. However, the elasticity of the ball and the surface it bounces on also play a significant role in the force and height of the bounce.

5. Can the angle of the bounce affect the force on a bouncing ball?

Yes, the angle of the bounce can affect the force acting on a bouncing ball. When a ball bounces at an angle, the force is distributed in two directions: perpendicular to the surface and parallel to the surface. The perpendicular force will determine the height of the bounce, while the parallel force will determine the distance the ball travels. As the angle of the bounce changes, the distribution of the force will also change, resulting in different heights and distances for the bounce.

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