The upward normal force exerted by the floor is 620 N on an elevator passenger who weighs 650 N. What is the magnitude of the acceleration?
Concept and reason
The concepts that are to be used to solve the given problem are Newton’s second law, net external force, normal force, and weight.
First calculate the mass of the passenger by using the relation between the weight and mass. After that, draw the free-body diagram for the forces exerted on the passenger. Finally, calculate the magnitude of the acceleration by using the free-body diagram and the Newton’s second law of motion.
Fundamentals
According to Newton’s second law of motion, the net force acting on an object of mass m produces an acceleration a. Mathematical form of Newton’s second law is as follows:
Answer:
The mass of the passenger is calculated by using the relation between the weight and mass.
Explanation:
As the earth’s gravity acts towards the center of the earth, the weight of the passenger is pointed in downward direction.
The normal force exerted by the floor on the passenger is pointed in upward direction and the gravitational force (weight) exerted on the passenger is pointed in downward direction. In this scenario, the net downward force (650 N) is greater than the net upward force (620 N). So, the acceleration of the elevator is pointed in downward direction. The free body diagram for the forces on the passenger is shown in the below figure.
Explanation:
The acceleration of the elevator has negative sign because the net downward force is greater than the net upward force. The negative sign means, the acceleration of the elevator is pointed in downward direction.
From the Newton’s second law, the net force exerted on the system of passenger and elevator along the vertical direction is,
Explanation:
The net force exerted on the passenger is equal to the vector sum of all the forces acting on the passenger. As the normal force is pointed up and the weight is pointed down, these two forces acting in opposite directions. So, the net force is the difference between the normal force and the weight.