Time hollow cylinder spends on ramp

In summary, the conversation discusses the problem of a hollow cylinder rolling on a horizontal surface and then reaching a 15 degree incline. The conversation covers solving for the height and length traveled up the incline, as well as determining the time it takes for the cylinder to reach the bottom. The use of energy conservation and average velocity are discussed in the solution process.
  • #1
cashmoney805
51
0

Homework Statement


A hollow cylinder (hoop) is rolling on a horizontal surface at speed v= 3.3 m/s when it reaches a 15 degree incline. (a) How far up the incline will it go? (b) How long will it be on the incline before it arrives back at the bottom?


Homework Equations


Energy conservation:
1/2 Iw^2 + 1/2mv^2 = mgh

v^2 = vo^2 +2ax
x=vot + .5at^2
v=vo+at


The Attempt at a Solution


I for this problem is (I think) 1/2 m (r1^2 + r2^2), but the r's cancel because w^2 = v^2/(r1^2 + r2^2)

So I believe the energy equation simplifies to .25v^2 + .5v^2 = gh

I solve and get h = .833 and so the length = .833/sin15 = 3.22
However, the book says the length is 4.29.

Also, after that I don't know where to go.

For time, I tried v=vo+at, for a I used 9.8sin 15 and t (up) I got 1.3s
However, the total t= 5.2 s

Thank you so much!
 
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  • #2
cashmoney805 said:

The Attempt at a Solution


I for this problem is (I think) 1/2 m (r1^2 + r2^2), but the r's cancel because w^2 = v^2/(r1^2 + r2^2)
Careful. Treat this as a thin hoop--with a single radius. (You're using a formula for a thick hollow cylinder. You'd have to set r1 = r2 to use that one.)

So I believe the energy equation simplifies to .25v^2 + .5v^2 = gh
You'll need to redo this, after fixing the above.

For time, I tried v=vo+at, for a I used 9.8sin 15 and t (up) I got 1.3s
However, the total t= 5.2 s
Careful--gravity is not the only force acting. A simpler way would be to figure out the average speed as it goes up the ramp.
 
  • #3
What other force is acting on it?

Ok, I treated the hoop as a thin one and now my equation is:

v^2 = gh
h = 1.1 m, so length is 1.1/sin15 = 4.29m woo!

Now for t... I don't really know what to use anymore :/
 
  • #4
cashmoney805 said:
What other force is acting on it?
Friction.

Ok, I treated the hoop as a thin one and now my equation is:

v^2 = gh
h = 1.1 m, so length is 1.1/sin15 = 4.29m woo!
Good.

Now for t... I don't really know what to use anymore
You know the distance. What's the average speed up the incline?
 
  • #5
Doc Al said:
Friction.


Good.


You know the distance. What's the average speed up the incline?
vo/2

Ah then do x/v = t. How do you know when to use average velocity though? I never seem to use that.
 

Related to Time hollow cylinder spends on ramp

1. How does the shape of the hollow cylinder affect the time spent on a ramp?

The shape of the hollow cylinder has a significant impact on the time it spends on a ramp. This is because the shape affects the distribution of mass and the moment of inertia, which determines how quickly the cylinder will roll down the ramp.

2. What factors influence the time a hollow cylinder spends on a ramp?

Besides the shape, there are other factors that can affect the time a hollow cylinder spends on a ramp. These include the mass of the cylinder, the angle of the ramp, and the friction between the ramp and the cylinder.

3. Is the time spent on a ramp the same for all hollow cylinders?

No, the time spent on a ramp can vary for different hollow cylinders. This is because each cylinder may have a different shape, mass, or other factors that can affect its movement on the ramp.

4. How can the time spent on a ramp be calculated for a hollow cylinder?

The time spent on a ramp for a hollow cylinder can be calculated using the principles of rotational motion. This involves using the moment of inertia, the angular velocity, and the angle of the ramp to determine the time it takes for the cylinder to roll down the ramp.

5. Can the time spent on a ramp be affected by external forces?

Yes, external forces such as air resistance or an uneven surface can affect the time a hollow cylinder spends on a ramp. These forces can slow down or speed up the cylinder's movement, resulting in a different amount of time being spent on the ramp.

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