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The force exerted by the floor of an ele...

The force exerted by the floor of an elevator on the foot of a person standing there is more than the weight of the person if the elevator is :

A

going up and slowing down

B

going up and slowing down

C

going down and slowing down

D

going down and speeding up

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the forces acting on a person standing in an elevator and determine under what conditions the normal force exerted by the elevator floor on the person exceeds their weight. ### Step-by-Step Solution: 1. **Identify the Forces Acting on the Person:** - The weight of the person (W) acts downward, which is given by the equation: \[ W = mg \] where \( m \) is the mass of the person and \( g \) is the acceleration due to gravity. - The normal force (N) exerted by the elevator floor acts upward. 2. **Set Up the Equation of Motion:** - According to Newton's second law, the net force acting on the person can be expressed as: \[ F_{\text{net}} = N - W \] - If the elevator is accelerating upward, the net force will be equal to the mass of the person multiplied by the acceleration (a) of the elevator: \[ F_{\text{net}} = ma \] - Therefore, we can write: \[ N - mg = ma \] 3. **Rearranging the Equation:** - Rearranging the equation gives us: \[ N = mg + ma \] - This shows that the normal force (N) is equal to the weight of the person (mg) plus the force due to the elevator's acceleration (ma). 4. **Condition for Normal Force to Exceed Weight:** - For the normal force to be greater than the weight of the person, we need: \[ N > mg \] - Substituting from our previous equation, we get: \[ mg + ma > mg \] - Simplifying this, we find: \[ ma > 0 \] - This indicates that the acceleration (a) must be greater than zero, meaning the elevator must be accelerating upward. 5. **Conclusion:** - The force exerted by the floor of the elevator on the foot of the person is more than the weight of the person if the elevator is accelerating upward. ### Answer: The elevator is accelerating upward.
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