What is the acceleration and displacement of a ball rolling up and down a hill?

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In summary, a ball starts rolling at an initial velocity of 4.00 m/s up a hill and 5 seconds later, it is rolling down the hill at 6.0 m/s. The question is asking for the ball's acceleration and displacement at 5.0s, assuming it did not start at the bottom of the hill. It is suggested to assume that the hill is at a constant angle and the component of gravity causing acceleration is constant at g.cos(theta). With the given information, it is possible to calculate the ball's acceleration.
  • #1
Carl_M
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A ball rolls at an initial velocity of 4.00 m/s up a hill. 5 seconds later it is rolling down the hill at 6.0 m/s. <---- What does the question mean? Did the ball roll up for 5 seconds and then started rolling down?

Find its acceleration
Find its displacement at 5.0s
 
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  • #2
Assume it didn't start at the bottom - so it mght be doing 6.0m/s below where it started
 
  • #3
So did the ball go up 4.00 m/s for 5 secs or go up the hill for 20 meters and then started to roll down at 6 m/s?
 
  • #4
the ball will be decelarating due to gravity then begins rolling downhill at increasing speed

I think you could assume the hill is at a constant angle so the component of gravity causing the acceleration is constant at g.cos(theta) for whatever theta is...

you know a time and a change in velocity so you should be able to get to what that acceleration is ...
 

Related to What is the acceleration and displacement of a ball rolling up and down a hill?

1. How does a ball roll up a hill?

A ball rolls up a hill due to the force of gravity. As the ball moves up the hill, the force of gravity pulls it back down. However, the ball also has forward momentum, which allows it to continue moving up the hill against the force of gravity.

2. What factors affect a ball's ability to roll up a hill?

The main factors that affect a ball's ability to roll up a hill are its mass, shape, and the steepness of the hill. A heavier ball will have more gravitational force pulling it down, making it harder to roll up the hill. A ball with a round shape will also have an easier time rolling up a hill compared to a ball with an irregular shape. Additionally, the steeper the hill, the harder it will be for the ball to maintain its momentum and continue rolling up.

3. Can a ball roll up any type of hill?

No, a ball cannot roll up any type of hill. In order for a ball to roll up a hill, there must be a balance between the forces of gravity pulling it down and the ball's momentum pushing it up. If the hill is too steep or the ball does not have enough momentum, it will not be able to roll up the hill.

4. What is the relationship between speed and a ball rolling up a hill?

The speed of the ball plays a crucial role in its ability to roll up a hill. A ball with a higher speed will have more momentum, making it easier for it to overcome the force of gravity and roll up the hill. However, if the ball is moving too fast, it may not have enough traction to maintain its grip on the hill and will roll back down.

5. Can a ball roll up a hill without any external forces?

In theory, a ball can roll up a hill without any external forces acting on it. This is because the ball already has potential energy due to its position on the hill, which can be converted into kinetic energy as it rolls up. However, in reality, there will always be some external forces such as friction and air resistance that will affect the ball's ability to roll up the hill.

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