# Circular motion of hoop and mass

• HardestPart
In summary, the mass slides along the hoop with negligible friction. When it is at an angle of 31 degrees, it has a speed of 5.23 m/s. The force with which it pushes on the hoop is F=mgR^2, where mg is the mass and R is the hoop's radius.
HardestPart

## Homework Statement

A mass M of 6.00E-1 kg slides inside a hoop of radius R=1.40 m with negligible friction. When M is at the top, it has a speed of 5.23 m/s. Calculate the size of the force with which the M pushes on the hoop when M is at an angle of 31.0°.

I have no idea from where to begin

I don't want you to do my homework,Can someone give me a hint?

Start by drawing a free body diagram. The use conservation of energy.

When I do the diagram
the total forces work on the mass is :
mg=mv^2/r

the low of energy is:
Mgh=1/2mv^2r

But I can't see how the angle is related to the sloution?

Can you use the conservation of energy to figure out the speed of the mass at 31 degrees? If so, do that first, and make sure you can get a numerical value.

Also, mg is not the only force on the block. N, the normal force, provides part of the centripetal acceleration.

But I don't know which force I have to do to components
I need cos ans sin right?
How can I do that?

I tried to find the speed of the mass at 31 degrees by:
N+mgcosa=mv^2/r
but i don't know what to but instead of N?

I tried to slove the question by :
N+mgcosa=mv^2/r
but i don't know what to put instead of N!?

HardestPart said:
I tried to slove the question by :
N+mgcosa=mv^2/r
but i don't know what to put instead of N!?

N is what you want to find.

I tried to fins the speed at angle 31 by:
I/2mv^2+mg2R=1/2mv^2+mgRsina
all m goes together
v^2+4gR=v^2+2gRsina
the answer i get from solving it i plugg into this:
N+mgcosa=mv^2/R
N=mv^2/Rsina-mgcosa
I get N=18.27N
but it is a wrong answer
Can you tell me where i went wrong?

## 1. What is the difference between uniform circular motion and non-uniform circular motion?

Uniform circular motion is when an object moves in a circle at a constant speed, while non-uniform circular motion is when an object moves in a circle at a changing speed. This could be due to an external force acting on the object or a change in the object's mass.

## 2. How does the radius of the hoop affect the circular motion of the mass?

The radius of the hoop does not affect the circular motion of the mass itself, as long as the mass is attached to the hoop and moves with it. However, the radius does affect the speed of the mass as it moves in the circle. A larger radius will result in a higher speed, while a smaller radius will result in a lower speed.

## 3. What is the relationship between the mass of the object and its centripetal force?

The centripetal force, or the force that keeps an object moving in a circular path, is directly proportional to the mass of the object. This means that as the mass increases, the centripetal force needed to keep it moving in a circle also increases.

## 4. Can a mass move in a circular path without a centripetal force?

No, a mass cannot move in a circular path without a centripetal force. According to Newton's First Law of Motion, an object will continue to move in a straight line at a constant speed unless acted upon by an external force. In circular motion, the centripetal force acts as the external force that keeps the object moving in a circular path.

## 5. How does the angle of the hoop affect the circular motion of the mass?

The angle of the hoop does not affect the circular motion of the mass, as long as the mass is attached to the hoop and moves with it. However, the angle may affect the direction of the centripetal force, which could cause the object to move in a different circular path. This can be seen in the case of a tilted or slanted hoop, where the centripetal force may act at an angle instead of perpendicular to the motion of the object.

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