Kinematics problem: Ball rolling off ramp & table

In summary, the conversation is about a problem involving a ball rolling off a table and the question of why the final velocity is not 0 when it reaches the floor. The discussion includes the use of equations and the misunderstanding of when the final velocity is 0.
  • #1
Bob Rudd
2
0

Homework Statement


http://imgur.com/0t8TVgq
http://imgur.com/0t8TVgq
upload_2016-4-25_17-2-26.png

[Image copy inserted by moderator]
Sorry about all the erase marks. My question is why is the final velocity not 0.

Homework Equations


V=Vo+at[/B]

The Attempt at a Solution


So the question is asking for the horizontal distance the ball travels before it hits the floor. First to solve this I decided to solve for time. To do this is used V=Vo+ at which I rearranged to t=(V-Vo)/a. Using just the vertical component, I decided the vertical velocity of the ball when it reaches the floor is 0. So I did (0-1)/-9.8 which gave me a time of .102. The book solved for the final distance first and then solved for time
My question is why is the final velocity no just 0. When it reaches the floor it can't have a positive velocity because it has stopped moving.
 
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  • #2
Bob Rudd said:

Homework Statement


http://imgur.com/0t8TVgq
http://imgur.com/0t8TVgq
Sorry about all the erase marks. My question is why is the final velocity not 0.

Homework Equations


V=Vo+at[/B]

The Attempt at a Solution


So the question is asking for the horizontal distance the ball travels before it hits the floor. First to solve this I decided to solve for time. To do this is used V=Vo+ at which I rearranged to t=(V-Vo)/a. Using just the vertical component, I decided the vertical velocity of the ball when it reaches the floor is 0. So I did (0-1)/-9.8 which gave me a time of .102. The book solved for the final distance first and then solved for time
My question is why is the final velocity no just 0. When it reaches the floor it can't have a positive velocity because it has stopped moving. [/B]

You know the ball falls for a certain distance when it rolls off the table. There's a SUVAT equation which deals with distance traveled under uniform acceleration, given an initial velocity. Why didn't you use this equation to find the time of the fall?
 
  • #3
Bob Rudd said:
the vertical velocity of the ball when it reaches the floor is 0
No, that is after it has hit the floor. The equation you used is only valid for constant acceleration, so only until it is just about to touch the floor.
 

Related to Kinematics problem: Ball rolling off ramp & table

1. How do you calculate the velocity of the ball as it rolls off the ramp?

The velocity of the ball can be calculated using the equation v = √(2gh), where v is the velocity, g is the acceleration due to gravity, and h is the height of the ramp. This equation assumes that there is no friction or air resistance acting on the ball.

2. What is the relationship between the angle of the ramp and the distance the ball travels?

The angle of the ramp affects the distance the ball travels because it determines the initial velocity of the ball. The steeper the ramp, the higher the initial velocity, resulting in a greater distance traveled. This is because the ball has more potential energy at a steeper angle, which is converted into kinetic energy as it rolls down the ramp.

3. How does the mass of the ball affect its motion on the ramp and table?

The mass of the ball has little effect on its motion on the ramp and table as long as there is no air resistance or friction present. This is because the mass of an object does not affect its acceleration due to gravity, which is the force causing the ball to roll down the ramp. However, a heavier ball may have more momentum and travel further on the table due to its increased inertia.

4. How do you determine the final velocity of the ball when it reaches the end of the table?

The final velocity of the ball when it reaches the end of the table can be calculated using the equation v = u + at, where v is the final velocity, u is the initial velocity (calculated from the ramp), a is the acceleration due to gravity, and t is the time it takes for the ball to reach the end of the table.

5. How does the height of the table affect the distance the ball travels on the floor?

The height of the table has a direct impact on the distance the ball travels on the floor. The higher the table, the longer the ball will have to fall before reaching the floor, resulting in a greater final velocity and thus a longer distance traveled. This can also be seen in the equation v = √(2gh), as the height of the table (h) is a factor in calculating the velocity (v) of the ball.

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