Finding velocity on flat part of ramp

In summary, Fieldguise found that the ball's final velocity is dependent on the height of the ramp, the inclination of the ramp, and the vertical height of the ramp.
  • #1
Fieldguise
5
0

Homework Statement


Greetings, I'm new here :).
Straight to my problem. I have a ramp. A ball accelerates down at varying angles, and then it reaches the flat part and travels only in the x-direction. I need to find the velocity of the ball as it moves on this flat part, as it is no longer accelerating.

Homework Equations


suvat, trigonometry

The Attempt at a Solution


First, I did this: 9.81×sin[itex]\theta[/itex]. This gives me the acceleration of the ball down the ramp at whatever angle.
(9.81×sin[itex]\theta[/itex])cos[itex]\theta[/itex] = x component of acceleration down ramp.

s(length of ramp)=1/2at^2
t= [itex]\sqrt{}2s/a[/itex]

By the time ball reaches flat part, vx=axt?
Here is an extremely simplistic model of the situation.
Ramp_zps928a0a9c.jpg
 
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  • #2
Hi, Fieldguise, welcome to physicsforums :) Your working all looks good so far. I would agree that just before the ball reaches the flat part, the horizontal speed is given by the x component of acceleration down the ramp, multiplied by the time it has been moving. But when the ball actually gets to the flat part of the ramp, what will happen to its speed? will its vertical motion be turned into horizontal motion, or will the vertical motion simply be lost and the energy given off as sound, etc ?
 
  • #3
BruceW said:
Hi, Fieldguise, welcome to physicsforums :) Your working all looks good so far. I would agree that just before the ball reaches the flat part, the horizontal speed is given by the x component of acceleration down the ramp, multiplied by the time it has been moving. But when the ball actually gets to the flat part of the ramp, what will happen to its speed? will its vertical motion be turned into horizontal motion, or will the vertical motion simply be lost and the energy given off as sound, etc ?

Yes, exactly. I don't how to determine how the y-component of the acceleration adds into the final horizontal velocity. The ball is smooth steel against a plastic ramp. Friction is small so the vertical motion definitely doesn't just disappear.

In some way, the vertical motion turns into horizontal motion. For example, when I angled the ramp steeply at about 75°, there was little acceleration in the x-direction, yet the ball still traveled further when it left the ramp than when the ramp was angled at 45°, at which point there was MORE acceleration in the x direction. So obviously the high vertical component of the acceleration at 75° added into the horizontal motion, I just don't know how to calculate it exactly, as I need an actual theoretical value.
 
  • #4
Fieldguise said:
Yes, exactly. I don't how to determine how the y-component of the acceleration adds into the final horizontal velocity. The ball is smooth steel against a plastic ramp. Friction is small so the vertical motion definitely doesn't just disappear.

In some way, the vertical motion turns into horizontal motion. For example, when I angled the ramp steeply at about 75°, there was little acceleration in the x-direction, yet the ball still traveled further when it left the ramp than when the ramp was angled at 45°, at which point there was MORE acceleration in the x direction. So obviously the high vertical component of the acceleration at 75° added into the horizontal motion, I just don't know how to calculate it exactly, as I need an actual theoretical value.

Here's an experiment I'd suggest: Roll the ball for various inclinations of the ramp but keep the vertical height of the ramp fixed for all inclinations. What do you notice about the final velocity of the ball?
 
  • #5
Sourabh N said:
Here's an experiment I'd suggest: Roll the ball for various inclinations of the ramp but keep the vertical height of the ramp fixed for all inclinations. What do you notice about the final velocity of the ball?

Should the velocity be the same each time? I can't do further testing as this was lab work. Keeping the vertical height fixed means I would have to change the length of the ramp for each test angle, and that is too many independent variables.
 
  • #6
Fieldguise said:
Should the velocity be the same each time?

Yes! What does this suggest for the final velocity? Does it depend on length of ramp? inclination of ramp? vertical height?

PS - Have you studied the concepts of work, energy and conservation of energy?
 
  • #7
Sourabh N said:
Yes! What does this suggest for the final velocity? Does it depend on length of ramp? inclination of ramp? vertical height?

PS - Have you studied the concepts of work, energy and conservation of energy?

Yes, I have studied those concepts.

So.. if the final velocity is constant when the vertical height of the ramp is also constant, it simply depends on the gravitational potential?

Then, by law of conservation of energy, the potential energy of the ball turns into kinetic energy. So I can use:

gΔh = 1/2v^2 , and solve for v? and I can ignore mass because I'm not actually finding energy?
 
  • #8
Fieldguise said:
Yes, I have studied those concepts.

So.. if the final velocity is constant when the vertical height of the ramp is also constant, it simply depends on the gravitational potential?

Then, by law of conservation of energy, the potential energy of the ball turns into kinetic energy. So I can use:

gΔh = 1/2v^2 , and solve for v? and I can ignore mass because I'm not actually finding energy?

Yes :smile:

I'm not sure what exactly your question was, but if that's what you intended to find, then good!
 
  • #9
Sourabh N said:
Yes :smile:

I'm not sure what exactly your question was, but if that's what you intended to find, then good!

Awesome! It isn't necessary to explain my whole procedure, but yea, I just needed to find the velocity on that part of the ramp.

Honestly, thank you a lot! I wasn't completely sure how to solve it and you helped me use logic to find the solution.
 
  • #10
No problem!
 

FAQ: Finding velocity on flat part of ramp

How do I calculate the velocity on a flat part of a ramp?

The velocity on a flat part of a ramp can be calculated using the formula v = d/t, where v is the velocity, d is the horizontal distance traveled, and t is the time taken to travel that distance.

What is the significance of finding the velocity on a flat part of a ramp?

Finding the velocity on a flat part of a ramp can help determine the speed and acceleration of an object as it moves along the ramp. It can also be used to predict the trajectory of the object and determine its potential energy.

Can the velocity on a flat part of a ramp be negative?

Yes, the velocity on a flat part of a ramp can be negative if the object is moving in the opposite direction of the ramp's incline. This indicates that the object is decelerating.

How does the angle of the ramp affect the velocity on a flat part?

The angle of the ramp affects the velocity on a flat part by influencing the acceleration of the object. A steeper ramp will result in a greater acceleration and therefore a higher velocity on the flat part, while a shallower ramp will result in a lower acceleration and velocity.

What factors can affect the accuracy of calculating velocity on a flat part of a ramp?

The accuracy of calculating velocity on a flat part of a ramp can be affected by factors such as air resistance, friction, and the mass of the object. These factors can cause discrepancies between the calculated velocity and the actual velocity of the object.

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