Question

I need help with questions B and C.

A person of mass m = 75 kg is at the highest point above the ground on a rotating Ferris wheel.

The normal force acting on the person at that point is nT = 615 N.

a) What is the value of the centripetal acceleration a? 1.6 m/s^2

b) What is the normal force acting on the person when she is at the lowest point on the rotating Ferris wheel?

c) If the Ferris wheel doubles its angular velocity, what is the normal force acting on the person when she is at the highest point on the Ferris wheel?

Answer 1

[AI-generated answer — Explain Bot]

To find the normal force acting on the person when she is at the lowest point on the rotating Ferris wheel (question B), we need to consider the forces acting on the person at that point.

At the lowest point, the person is experiencing both the force of gravity pulling her downwards (mg) and the force of the centripetal acceleration pushing her towards the center of the Ferris wheel.

The normal force (nB) acts perpendicular to the surface on which the person is sitting, and it balances the force of gravity to keep the person in equilibrium.

To find the normal force, we can use the equation for vertical equilibrium:

nB - mg = 0

Since we know the mass of the person (m = 75 kg) and the acceleration due to gravity (g = 9.8 m/s^2), we can substitute these values into the equation:

nB - (75 kg)(9.8 m/s^2) = 0

Simplifying the equation:

nB = (75 kg)(9.8 m/s^2)

Calculating this:

nB = 735 N

Therefore, the normal force acting on the person when she is at the lowest point on the rotating Ferris wheel is 735 N.

Now let's move on to question C.

To find the normal force acting on the person when she is at the highest point on the Ferris wheel after it has doubled its angular velocity (question C), we need to consider the new forces acting on the person.

When the angular velocity doubles, the centripetal acceleration also doubles, but the force of gravity remains the same.

The normal force (nC) at the highest point can be found using the equation for vertical equilibrium:

nC - mg = 0

We already know the mass of the person (m = 75 kg) and the acceleration due to gravity (g = 9.8 m/s^2). Now, we need to find the new centripetal acceleration (ac) at the highest point after the Ferris wheel doubles its angular velocity.

Given that the initial centripetal acceleration is a = 1.6 m/s^2, we can use the following relationship between angular velocity (ω) and centripetal acceleration:

ac = ω^2 * r

Since the radius of the Ferris wheel remains constant, doubling the angular velocity will result in doubling the centripetal acceleration:

ac = 2 * 1.6 m/s^2
= 3.2 m/s^2

Substituting the values into the equation for vertical equilibrium:

nC - (75 kg)(9.8 m/s^2) = 0

Simplifying the equation:

nC = (75 kg)(9.8 m/s^2)

Calculating this:

nC = 735 N

Therefore, the normal force acting on the person when she is at the highest point on the Ferris wheel after it doubles its angular velocity is 735 N.