Normal Force and Energy

[Soaring Crane]

A small mass m slides without friction along the looped apparatus.

If the mass is to remain on the track at all times, even at the top of the loop of radius r.

If the release height is 2h,

calculate the normal force

a. exerted by the the track at the bottom of the loop. 11mg
b. exerted by the track at the top of the loop. 5 mg
c. exerted by the track after the block exits the loop onto the flat section. mg

I know the conservation of mechanical energy is used, but I do not know how to tie it in with solving to find the normal force.

Please help me in any way possible. Thanks.

How do you know when to use the conservation of energy formula and the work energy theorem?

[arildno]

The component of gravity along the normal+plus the normal force must yield the centripetal acceleration of the object.

[dekoi]

How do you know when to use the conservation of energy formula and the work energy theorem?

When there is only one force acting on the object, you can use the Work Energy Theorem (for example, a cart along a path with neglible friction). However, when a spring is used, with e.g. Elastic energy and gravitational energy (kinetic as well), you must use the conservation of energy.

[Soaring Crane]

I know at the top that F_n + mg = (mv^2)/r, but must I set it up in accord with the conservation of energy theorem. If so, how?

[Skomatth]

Determine v by using conservation of energy.