Mass rotating in a hoop

In summary, the force with which the mass M pushes on the hoop when at an angle of 44.0° is 26.2026 N, taking into account both the force exerted by the hoop and the force of gravity.
  • #1
Staerke
12
0

Homework Statement


A mass M of 5.20E-1 kg slides inside a hoop of radius R=1.10 m with negligible friction. When M is at the top, it has a speed of 4.25 m/s. Calculate the size of the force with which the M pushes on the hoop when M is at an angle of 44.0°.


Homework Equations


E = Pe + Ke
Pe = m * g * h
Ke = 1/2 * m * v^2
F=mv^2/r


The Attempt at a Solution



Alright so energy at the top = Pe + Ke
So m*g*h + 1/2*m*v^2 = 11.2226 + 4.69625 = 15.9189

The energy in the bottom is going to be equal to the energy at the top
The height at the bottom is R-Rcos(44) = .295511
15.9189 = .52*9.81*.29511 + .5*.52*v^2
V=7.44503

Centripital force = mv^2/r, so .52*7.44503^2/1.1 = 26.2026 N

But this is wrong. Now I thought it might be reduced due to gravity.
so F=26.2026-m*g*cos(44) = 22.5331
Neither answer works.
Help?
 
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  • #2
Nobody? :(
 
  • #3
Staerke said:

Homework Statement


A mass M of 5.20E-1 kg slides inside a hoop of radius R=1.10 m with negligible friction. When M is at the top, it has a speed of 4.25 m/s. Calculate the size of the force with which the M pushes on the hoop when M is at an angle of 44.0°.

Homework Equations


E = Pe + Ke
Pe = m * g * h
Ke = 1/2 * m * v^2
F=mv^2/r

The Attempt at a Solution



Alright so energy at the top = Pe + Ke
So m*g*h + 1/2*m*v^2 = 11.2226 + 4.69625 = 15.9189

The energy in the bottom is going to be equal to the energy at the top
The height at the bottom is R-Rcos(44) = .295511
15.9189 = .52*9.81*.29511 + .5*.52*v^2
V=7.44503

Centripetal force = mv^2/r, so .52*7.44503^2/1.1 = 26.2026 N

But this is wrong. Now I thought it might be reduced due to gravity.
so F=26.2026-m*g*cos(44) = 22.5331
Neither answer works.
Help?
Sorry that nobody responded sooner.

What is the angle 44.0° in relation to.

Your answer looks right for centripetal force, assuming the velocity is right.

The radial component of the net force exerted on M is equal to Mv2/r, the centripetal force. However, there are two contributions to this force.
One is the force exerted on M by the hoop.

The other is gravity. There a component of the gravitational force which is in the radial direction. This is what you haven't taken into account.​
 

1. What is the concept of a mass rotating in a hoop?

The concept of a mass rotating in a hoop refers to the motion of a physical object or particle that is moving along a circular path within a hoop-shaped structure. This type of motion is known as circular motion, and it is characterized by a constant radius and a changing velocity.

2. What are the factors that affect the motion of a mass rotating in a hoop?

The motion of a mass rotating in a hoop is influenced by several factors, including the mass of the object, the radius of the hoop, the speed of rotation, and the force applied to the object. These factors determine the centripetal force and the angular velocity of the object.

3. How does the centripetal force affect the motion of a mass rotating in a hoop?

The centripetal force, which is directed towards the center of the circle, is responsible for keeping the mass rotating in a hoop in a circular path. It is proportional to the mass of the object, the square of its velocity, and inversely proportional to the radius of the hoop. An increase in centripetal force will result in an increase in the speed of rotation.

4. What is the difference between tangential velocity and angular velocity in the context of a mass rotating in a hoop?

Tangential velocity refers to the speed at which the mass is moving along the circular path, while angular velocity refers to the rate at which the object is rotating around the center of the hoop. Tangential velocity is measured in linear units, such as meters per second, while angular velocity is measured in radians per second.

5. How is the conservation of angular momentum applied in the motion of a mass rotating in a hoop?

The principle of conservation of angular momentum states that the total angular momentum of a system remains constant unless an external torque is applied. In the context of a mass rotating in a hoop, this means that the product of the mass, radius, and angular velocity will remain constant as long as there is no external torque acting on the object.

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