What Forces Act on a Mass Sliding Inside a Hoop?

[Staerke]

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?

 

[Staerke]

Nobody? :(

 

[SammyS]

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.​