Conservatino of Momentum: Bowling Ball and Earth

In summary, the conversation discusses a 7.00kg bowling ball being dropped from a height of 3.00m. It then asks for the speed of the Earth as it meets the ball before it hits the ground, using the mass of the Earth as 5.98 x 10^23 kg. The conversation also mentions using this answer to justify ignoring the motion of the Earth when dealing with the motions of terrestrial objects. The solution involves finding the velocity of the bowling ball before impact using the equation Vf^2=Vi^2 + 2ad and then using conservation of momentum to find the final velocities of both the bowling ball and Earth.
  • #1
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Homework Statement


A 7.00kg bowling ball is dropped from rest at an initial height of 3.00m.
(a) What is the speed of the Earth coming up to meet the ball just before the ball hits the ground? Use 5.98 x 10^23 kg as the mass of the Earth
(b)Use your answer to part (a) to justify ifnoring t he motion of the Earth when dealing with the motions ofs terrestrial objects.


Homework Equations


p=mv
F=p/t
m1v1i+m2v2i=m1v1f+m2v2f


The Attempt at a Solution


So here is my attempt. i thought I should find the velocity of the bowling ball when the it comes in contact with the Earth first so using Vf^2=Vi^2 + 2ad:

Vf^2 = 0 +2(9.8)(3)
Vf^2 = 58.8
Vf = 7.67 m/s

so after that, i have:
m1=7.00kg
v1i=2.67 m/s
m2=5.8 x 10^24

it looks like I'm looking for V2i for part (a) so i need to find V1f and V2f.
Thats where I'm stuck. Anyone know this one?
 
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  • #2
Apply conservation of momentum. Assume that both Earth and bowling ball start out at rest.
 
  • #3


Your approach to finding the velocity of the bowling ball when it hits the ground is correct. However, to find the speed of the Earth coming up to meet the ball, we need to consider the conservation of momentum. The initial momentum of the system (bowling ball and Earth) is 0, as both objects are at rest. When the ball is dropped, it gains momentum while the Earth gains an equal amount of momentum in the opposite direction. So, we can use the equation m1v1i = m1v1f + m2v2f to find the velocity of the Earth.

m1v1i = 7.00kg * 2.67 m/s = 18.69 kgm/s

Since the mass of the Earth (m2) is much larger than the mass of the bowling ball, we can assume that the velocity of the Earth (v2f) is negligible compared to the velocity of the bowling ball (v1f). Therefore, we can ignore the velocity of the Earth when dealing with the motion of the bowling ball.

As for justifying this assumption, we can consider the ratio of the masses of the two objects. The mass of the Earth (5.98 x 10^23 kg) is approximately 8.54 x 10^19 times larger than the mass of the bowling ball (7.00 kg). This means that the Earth's momentum is 8.54 x 10^19 times larger than the bowling ball's momentum. In comparison, the Earth's velocity would be 8.54 x 10^19 times smaller than the bowling ball's velocity. Therefore, the Earth's velocity can be considered negligible when dealing with the motion of the bowling ball.

In conclusion, the conservation of momentum principle allows us to justify ignoring the motion of the Earth when dealing with the motion of terrestrial objects such as the bowling ball in this scenario.
 

1. How does the conservation of momentum apply to a bowling ball and the Earth?

The conservation of momentum states that the total momentum of a system remains constant, unless acted upon by an external force. In the case of a bowling ball and the Earth, the momentum of the bowling ball and the Earth combined remains constant as long as there are no external forces acting on the system.

2. Can the momentum of a bowling ball change while it is rolling on the Earth?

Yes, the momentum of the bowling ball can change while it is rolling on the Earth if there are external forces acting on the system. For example, if someone were to push the bowling ball, its momentum would change as it gains or loses velocity.

3. How does the mass of the bowling ball affect the conservation of momentum?

The mass of the bowling ball affects the conservation of momentum by determining how much momentum it contributes to the system. A heavier bowling ball will have a greater momentum compared to a lighter bowling ball, but the total momentum of the system will remain constant.

4. Does the speed of the bowling ball affect the conservation of momentum?

Yes, the speed of the bowling ball affects the conservation of momentum because momentum is directly proportional to an object's mass and velocity. A bowling ball moving at a faster speed will have a greater momentum compared to a bowling ball moving at a slower speed, but the total momentum of the system will remain constant.

5. What other factors can affect the conservation of momentum in the bowling ball and Earth system?

In addition to mass and velocity, other factors that can affect the conservation of momentum in the bowling ball and Earth system include external forces such as friction and air resistance. These forces can cause a change in the momentum of the bowling ball and the Earth, but the total momentum of the system will still remain constant unless acted upon by an external force.

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