A aeroplane with a mass of 9940 kg completes a vertical loop of radius 155m/s. What normal force does the airplane seat exert on the 92 kg pilot at the top of the loop and at the bottom of the loop?

We need the centripetal acceleration

Ac = v^2/r
you only gave one, the speed I think

at the top
force on seat = m (v^2/r - g)
at the bottom
m (v^2/r + g)

To find the normal force exerted by the airplane seat on the pilot at the top and bottom of the loop, we need to consider the net force acting on the pilot.

At the top of the loop, the pilot is moving in a circular path with the airplane. The gravitational force and the normal force act in the same direction, towards the center of the loop. So the net force is the sum of these two forces:

net force = gravitational force + normal force

The gravitational force is given by the formula:

gravitational force = mass * gravitational acceleration

where the gravitational acceleration, g, is approximately 9.8 m/s².

For the pilot at the top of the loop, the net force should provide the centripetal force required to ensure circular motion. The centripetal force is given by:

centripetal force = mass * (velocity^2 / radius)

Substituting the given values:

mass = 92 kg

velocity = 0 m/s (at the top of the loop, the velocity is momentarily zero)

radius = 155 m

Using this information, we can find the required net force. Rearranging the centripetal force formula, we get:

net force = mass * (velocity^2 / radius)

net force = 92 kg * (0^2 / 155 m)

net force = 0 N

Therefore, at the top of the loop, the net force on the pilot is zero, which means the normal force exerted by the seat is also zero.

At the bottom of the loop, the situation is different. Here, the gravitational force and the normal force act in the opposite direction. The net force is still the sum of these two forces:

net force = gravitational force + normal force

Using the same formula for the gravitational force:

gravitational force = mass * gravitational acceleration

and the formula for the centripetal force:

centripetal force = mass * (velocity^2 / radius)

we can find the net force at the bottom.

At the bottom of the loop, the velocity is not zero. Instead of using 0 m/s for the velocity, we need to consider the minimum velocity required for the airplane to complete the loop, which occurs at the top of the loop. We can use the formula for centripetal force, rearrange it, and find the minimum velocity:

centripetal force = mass * (velocity^2 / radius)

mass * (velocity^2 / radius) = mass * g + normal force

velocity^2 / radius = g + (normal force / mass)

velocity^2 = (g + (normal force / mass)) * radius

velocity^2 = (9.8 m/s² + (normal force / 92 kg)) * 155 m

To complete the loop, the minimum velocity is such that the net force at the bottom is zero, which means:

gravitational force + normal force = 0

mass * gravitational acceleration + normal force = 0

92 kg * 9.8 m/s² + normal force = 0

901.6 N + normal force = 0

normal force = -901.6 N

Therefore, at the bottom of the loop, the normal force exerted by the seat on the pilot is -901.6 N, indicating that it is directed upwards.