How would you include gravity in a momentum problem?

In summary, the conversation discusses the scenario of a big ball with mass m1 and a small ball with mass m2 being dropped from a height of h and colliding in an elastic collision. The problem at hand is to determine the heights each ball will reach after the collision. The suggested approach is to use gravitational potential energy and energy conservation, taking into account the fact that the collision is elastic. It is also mentioned that details about the elasticity of the balls will help in solving the problem.
  • #1
Rnotaria
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0

Homework Statement



Say you have a big ball of mass m1 and a little ball on top of that of mass m2 (assume they are a small distance apart, like 1mm). Now let's drop these from a height of h so that the big ball will bounce off the ground and collide into the little ball in an elastic collision.

Homework Equations



p=mv

The Attempt at a Solution



I know gravity would play a key role in this example but how would you perform calculations with it? I know F=p/t and momentum will not be conserved since there is an external force (gravity) so knowing this, how can you determine how high each ball will rise after the collision? I was thinking of turning the force of gravity into momentum by multiplying with time but that is an unknown variable.
 
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  • #2
Use gravitational potential energy and energy conservation. Consider the two states of the system: the initial state is before collision and the final state is after collision. Use the fact that the collision is elastic to draw conclusions.

What is the actual problem; what are you asked to calculate?
 
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Likes CWatters
  • #3
Perhaps break it down into stages. If you have details about the elasticity of the balls it should be straight forward to work out the velocities of both balls just after the larger ball has bounced. eg when the large ball is on the way up and the small ball is still falling. Then with luck you have a simple collision between two balls to solve.
 

Related to How would you include gravity in a momentum problem?

1. How does gravity affect momentum?

Gravity is a fundamental force that affects the motion of all objects in the universe. It is responsible for the acceleration of objects towards the Earth's surface and is a crucial factor in understanding momentum. Without taking gravity into account, the momentum of an object will not be accurate.

2. Is gravity always included in momentum problems?

No, gravity is not always included in momentum problems. It depends on the specific situation and the objects involved. If the objects are not affected by gravity or if the effects of gravity are negligible, then it may not be necessary to include it in the momentum calculations.

3. How do you calculate the momentum of an object with gravity?

To calculate the momentum of an object with gravity, you will need to use the formula p = m x v + m x g x t, where p is momentum, m is mass, v is velocity, g is the acceleration due to gravity (9.8 m/s^2), and t is time. This formula takes into account both the linear and gravitational components of momentum.

4. What are some common mistakes when including gravity in momentum problems?

One common mistake is forgetting to include the gravitational component in the momentum calculations. Another mistake is using the incorrect value for acceleration due to gravity, as it can vary depending on the location (e.g. Earth's gravity is 9.8 m/s^2, while the moon's gravity is 1.62 m/s^2).

5. Can gravity affect the direction of momentum?

Yes, gravity can affect the direction of momentum. When an object is moving in a curved path, the force of gravity may cause it to change direction and therefore affect the momentum. This is why it is important to consider both the linear and gravitational components when calculating momentum in a problem.

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