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A man is on a Ferris wheel that rotates with a constant scalar velocity v = 5.90m/s. The man's mass is m = 75.4 kg and the Ferris wheel has a radius R = 9.45 m. Determine the value of the magnitude of the normal force acting on the man when he is at the highest point of the trajectory, when he is at the lowest point of the trajectory, and what is the period of movement.

User Willsteel
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Answer and Explanation:

To determine the value of the magnitude of the normal force acting on the man at the highest and lowest points of the trajectory, we need to consider the forces acting on the man and apply Newton's second law.

At the highest point of the trajectory, the man experiences two forces: the gravitational force pulling him downward and the normal force pushing him upward.

Step 1: Calculate the gravitational force.

Gravitational force = mass * acceleration due to gravity

Step 2: Calculate the net force.

Net force = gravitational force

Step 3: Calculate the normal force.

Normal force = net force

At the lowest point of the trajectory, the man experiences the gravitational force pulling him downward and the normal force pushing him upward.

Step 4: Calculate the net force.

Net force = gravitational force

Step 5: Calculate the normal force.

Normal force = net force

To determine the period of movement, we can use the formula for the period of circular motion.

Step 6: Calculate the period of movement.

Period = 2π * radius / velocity

Given:

Scalar velocity (v) = 5.90 m/s

Mass (m) = 75.4 kg

Radius (R) = 9.45 m

Acceleration due to gravity (g) = 9.8 m/s²

Step 1: Calculate the gravitational force.

Gravitational force = 75.4 kg * 9.8 m/s² = 739.92 N

Step 2: Calculate the net force.

Net force = 739.92 N

Step 3: Calculate the normal force at the highest point.

Normal force = 739.92 N

Step 4: Calculate the net force.

Net force = 739.92 N

Step 5: Calculate the normal force at the lowest point.

Normal force = 739.92 N

Step 6: Calculate the period of movement.

Period = 2π * 9.45 m / 5.90 m/s ≈ 10.08 s

Therefore, the magnitude of the normal force acting on the man is 739.92 N at both the highest and lowest points of the trajectory. The period of movement is approximately 10.08 seconds.

User Bleeeah
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