A daredevil is riding a motorcycle on the inside of a spherical metal cage of radius 9.7 meters. The total mass of the person and motorcycle is 79.2 kg. If he is to make a vertical circle within the cage at some constant speed, v, what normal force, in Newtons, does he feel at the bottom of the cage if he is to just barely make it around the top of cage (such that the normal force is just zero at the top) ? (Just think of it as one object with a mass of 79.2 kg going around the circle.)

HELP ME . HELP ME . PLEASE !!!

First question: 2 M g

at the bottom of the cage, if going fast enough to barely be in contact at the top.

Second question:

M V^2/R - M g = 0

Cancel the M and solve for V.

To find the normal force experienced by the daredevil at the bottom of the cage, we need to consider the forces acting on the person and the motorcycle at that point.

The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the daredevil is at the bottom of the cage, so the normal force is the force exerted by the cage on the daredevil.

To just barely make it around the top of the cage, the centrifugal force at the top must be equal to the gravitational force acting on the daredevil at the bottom. At the top of the cage, the normal force is zero because the centrifugal force is equal to the gravitational force, so it cancels out.

To calculate the normal force at the bottom, we need to first determine the speed at which the daredevil needs to travel on the inside of the cage.

Since the centripetal force is provided by the normal force, we can use the centripetal force equation:

F_c = m * a_c

Where F_c is the centripetal force, m is the mass of the daredevil and the motorcycle, and a_c is the centripetal acceleration.

The centripetal force can also be expressed as:

F_c = m * v^2 / r

Where v is the speed and r is the radius of the circular path.

Setting the gravitational force equal to the centripetal force at the bottom:

m * g = m * v^2 / r

Rearranging the equation to solve for v:

v^2 = r * g

v = sqrt(r * g)

Substituting the given values:

v = sqrt(9.7 m * 9.8 m/s^2)

v ≈ 9.82 m/s

Now that we have the speed, we can calculate the normal force at the bottom of the cage.

At the bottom of the cage, the centrifugal force provides the entire normal force since there is no contribution from gravity.

The centrifugal force is given by:

F_cf = m * v^2 / r

Substituting the given values:

F_cf = 79.2 kg * (9.82 m/s)^2 / 9.7 m

F_cf ≈ 79.66 N

Therefore, the daredevil feels a normal force of approximately 79.66 Newtons at the bottom of the cage to just barely make it around the top.