Calculating Forces on an 80kg Man on a Ferris Wheel

[HawKMX2004]

The question states that in an amusement park the Ferris wheel rotates at .4 rad/s An 80 kg man sits on a scale as he rides at a distance of 9 m from the axis of rotation. What does the scale read when the man is A.) At the top of the ride and B.) at the bottom of the ride.

All me and my partner have is that the Velocity of the ferris wheel is 3.6 m/s. We are at a total loss for the rest. Help Please?

 

[vsage]

Start by seeing how much centripetal force is required for the man to remain in circular motion with the ferris wheel. Consider how this lack of centripetal force affects the resultant force of it and gravity at the top and bottom of the ferris wheel.

 

[wais]

To calculate the forces on the 80kg man on the Ferris wheel, we can use the equation F=ma, where F is the force, m is the mass, and a is the acceleration. In this case, the acceleration is the centripetal acceleration, given by a=v^2/r, where v is the velocity and r is the distance from the axis of rotation.

A) At the top of the ride, the man is at the highest point, so the distance from the axis of rotation is 9m. The velocity of the Ferris wheel remains constant at 3.6 m/s, so the centripetal acceleration is a=v^2/r=(3.6 m/s)^2/9m=1.44 m/s^2.

Using F=ma, we can calculate the force on the man at the top of the ride as F=(80 kg)(1.44 m/s^2)=115.2 N. This is the total force acting on the man, which includes his weight and the centripetal force.

Since the man is sitting on a scale, the scale will read the total force acting on him, which is 115.2 N.

B) At the bottom of the ride, the man is at the lowest point, so the distance from the axis of rotation is 9m. The velocity of the Ferris wheel remains constant at 3.6 m/s, so the centripetal acceleration is a=v^2/r=(3.6 m/s)^2/9m=1.44 m/s^2.

Using F=ma, we can calculate the force on the man at the bottom of the ride as F=(80 kg)(1.44 m/s^2)=115.2 N. However, at the bottom of the ride, the man's weight is acting in the opposite direction of the centripetal force, so we need to subtract his weight from the total force.

The man's weight is given by mg=(80 kg)(9.8 m/s^2)=784 N. Therefore, the net force on the man at the bottom of the ride is 115.2 N - 784 N = -668.8 N. This means that the scale will read a negative value, indicating that the man is experiencing a downward force.

In summary, the scale will read 115.2 N when the man is at the top of the ride and -