Calculating Velocity at the Bottom of a Quarter Circle Track

In summary, the conversation is discussing the calculation of the velocity of a block at the bottom of a frictionless track, given its initial downward velocity and the track's radius. The conversation includes a discussion of the equations for translational and rotational kinetic energy, gravitational potential energy, and the moment of inertia. Ultimately, it is determined that the velocity at the bottom of the track can be calculated using the equation vf2=vi2+ghinitial, and that the radius of the track is equal to the initial height of the block.
  • #1
tennisgirl92
43
1

Homework Statement


A block of mass 10kg starts at the top of a frictionless track which forms a quarter circle with radius 10m. It is given an initial downward velocity of 10m/s. What is the velocity at the bottom of the track?

Homework Equations


KEtranslational, f+ KErotational, f+PEf=KEtranslational, i+KErotational, i+ PEf
KE, rotational=1/2Iw2
KE, translational=1/2mv2
PE=mgh
I=MR2
w=v/r

The Attempt at a Solution


I believe the initial equation would be set up like this.
1/2mvf2+ 1/2 MR2(V/R)2+mghf=1/2mvi2+1/2 MR2(V/R)2+mghi

which would then reduce to:
vf2=vi2+ghinitial

This does not seem like the likely way to do it because we are not given the height of the mass at the top. Should I be using the rotational and translational KE in the equation? At what point is it rotational and what point translational?
 
Physics news on Phys.org
  • #2
tennisgirl92 said:
vf2=vi2+ghinitial

This does not seem like the likely way to do it because we are not given the height of the mass at the top.

Look carefully.

tennisgirl92 said:
Should I be using the rotational and translational KE in the equation? At what point is it rotational and what point translational?

Why would it rotate? When does something rotate?
 
  • #3
Mastermind01 said:
Look carefully.Why would it rotate? When does something rotate?

Would the radius be the initial height?

When it is rolling? I'm not exactly sure.
 
  • #4
tennisgirl92 said:
Would the radius be the initial height?

That is correct.

tennisgirl92 said:
When it is rolling? I'm not exactly sure.

Try and think intuitively if you don't know the physics behind it.
 
  • #5
Mastermind01 said:
That is correct.
Try and think intuitively if you don't know the physics behind it.
Ok, now I see how to do this. I obtained 17.2 m/s, which is correct. Thank you!

However, I still don't see how the radius could be equal to the height of the ramp. There is a picture provided that looks like a skateboard ramp, with a strict vertical height and then the inside being curved with a radius. The vertical height does not look equal to the radius, even though I know this is not to scale.
 
  • #6
Does the picture below look like the picture you have of the skateboard ramp? Is the quarter circle oriented like that?
Quarter circle track.jpg
 
  • Like
Likes Mastermind01
  • #7
TomHart said:
Does the picture below look like the picture you have of the skateboard ramp? Is the quarter circle oriented like that?View attachment 197493
yes, it is just like that, except flipped so that the curve is on the right and height on the left.
 
  • #8
So does it make sense to you that the radius = height?
 
  • #9
Yes, I do see it now-my picture did not have the radius being pointed horizontally and vertically, just down the middle. Thank you for all your help!
 
  • Like
Likes TomHart

FAQ: Calculating Velocity at the Bottom of a Quarter Circle Track

1. What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, it can only be transferred or transformed from one form to another.

2. Why is the conservation of energy important?

The conservation of energy is important because it is a fundamental law of physics that applies to all physical systems. It helps us understand and predict the behavior of energy in various forms, and it also plays a crucial role in many technological advancements.

3. How does energy conservation impact the environment?

Energy conservation plays a crucial role in protecting the environment. By reducing our energy consumption, we can decrease our carbon footprint and help mitigate climate change. It also helps preserve natural resources and reduces pollution.

4. What are some examples of energy conservation?

There are many ways to conserve energy, including turning off lights and electronics when not in use, using energy-efficient appliances, using public transportation or carpooling, and using renewable energy sources like solar or wind power.

5. How can we promote energy conservation?

We can promote energy conservation by raising awareness about its importance and educating others about simple ways to reduce energy consumption. Governments and organizations can also implement policies and incentives to encourage energy conservation and the use of renewable energy sources.

Similar threads

Conservation of energy problem: Ball rolling down inclined plane and then through a loop-the-loop
Replies
10
Views
1K
Starting height of marble rolling around a loop the loop
Replies
12
Views
11K
Velocity of a hollow cylinder at the bottom of an incline
Replies
9
Views
3K
Speed of block as cylinder reaches bottom of circular track.
Replies
11
Views
6K
Centripetal motion, the tension at the bottom of a circle
Replies
7
Views
4K
Conservation of Angular Momentum & Energy question
Replies
3
Views
2K
How does the kinetic energy of a swinging ball change with respect to height?
Replies
21
Views
2K
Maximizing Height Above Circle Center with Energy Conservation
Replies
9
Views
3K
Did I Calculate the Velocity of a Cylinder Correctly Using Energy?
Replies
4
Views
949
Energy analysis of a particle moving in a shrinking circle
Replies
17
Views
3K

Hot Threads

Recent Insights

Back
Top