Distance the hoop travels up the incline

In summary, a ring with specific mass, inner and outer radii, and initial speed is rolling up an inclined plane at a given angle. It will continue up the plane for a certain distance before rolling back down. The problem can be solved using torque and energy equations, with the latter being a simpler and more efficient approach.
  • #1
vbrasic
73
3

Homework Statement


A ring (hollow cylinder) of mass 2.61kg, inner radius 6.35cm, and outer radius 7.35cm rolls (without slipping) up an inclined plane that makes an angle of θ=36.0°, as shown in the figure below. At the moment the ring is at position x = 2.19m up the plane, its speed is 2.61m/s. The ring continues up the plane for some additional distance and then rolls back down. It does not roll off the top end. How much further up the plane does it go?

Homework Equations


##T=RF=I\alpha##
##\omega_f^2=\omega_i^2+2\alpha d##

The Attempt at a Solution


My proposed way to solve the problem is this:

I calculated the gravitational force down the ramp. This force is 15.034 N. It exerts a torque on the hoop of ##15.034N\times 0.0735 m##. Torque is also equal to ##I\alpha##. I can calculate ##I##. Dividing by it will give me angular acceleration. Then I can solve for the angular distance it takes for the hoop to stop rolling up the hill. Does this approach make sense?
 
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  • #2
vbrasic said:

Homework Statement


A ring (hollow cylinder) of mass 2.61kg, inner radius 6.35cm, and outer radius 7.35cm rolls (without slipping) up an inclined plane that makes an angle of θ=36.0°, as shown in the figure below. At the moment the ring is at position x = 2.19m up the plane, its speed is 2.61m/s. The ring continues up the plane for some additional distance and then rolls back down. It does not roll off the top end. How much further up the plane does it go?

Homework Equations


##T=RF=I\alpha##
##\omega_f^2=\omega_i^2+2\alpha d##

The Attempt at a Solution


My proposed way to solve the problem is this:

I calculated the gravitational force down the ramp. This force is 15.034 N. It exerts a torque on the hoop of ##15.034N\times 0.0735 m##. Torque is also equal to ##I\alpha##. I can calculate ##I##. Dividing by it will give me angular acceleration. Then I can solve for the angular distance it takes for the hoop to stop rolling up the hill. Does this approach make sense?
Just FYI, there IS no "figure below"
 
  • #3
vbrasic said:
Does this approach make sense?
Can you provide expressions instead of numbers? That way it would be easier to check your work.
 
  • #4
While you can do it by using a force and torque analysis, there are many things that you need to be careful with, things that we cannot tell whether you got them right or not unless you provide your working. Also, it is (quite a lot) simpler to use energy arguments.
 
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What is the definition of "Distance the hoop travels up the incline"?

The distance the hoop travels up the incline refers to the vertical displacement of the hoop as it moves along the incline. It is typically measured in meters or feet.

How is the distance the hoop travels up the incline calculated?

The distance the hoop travels up the incline can be calculated using the formula d = sin(theta) * l, where d is the distance traveled, theta is the angle of the incline, and l is the length of the incline. This formula assumes that there is no friction or air resistance affecting the movement of the hoop.

What factors affect the distance the hoop travels up the incline?

The distance the hoop travels up the incline can be affected by various factors such as the angle of the incline, the mass of the hoop, the force applied to the hoop, and the presence of friction or air resistance. These factors can either increase or decrease the distance traveled by the hoop.

Why is the distance the hoop travels up the incline an important concept in physics?

The distance the hoop travels up the incline is an important concept in physics because it helps us understand the relationship between force, energy, and motion. By studying the distance the hoop travels up the incline, we can also learn about concepts such as work, potential energy, and kinetic energy.

How can the distance the hoop travels up the incline be used in real-world applications?

The concept of distance the hoop travels up the incline can be applied in various real-world scenarios such as designing ramps and slides, calculating the efficiency of machines, and analyzing the movement of objects on inclined surfaces. It is also a fundamental concept in fields such as engineering, sports, and transportation.

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