A person is standing in an elevator, which is accelerating upwards. What can you say about the relationship between the force due to gravity mg and the normal force N (both on the person)?
a) N > mg
b) N = mg
c) N < mg (but not zero)
d) N = 0
I picked d because the m in mg would be elevator + person so the force would be waaaaay higher than in N.
The correct answer is (b) N = mg.
In this scenario, the person is in an elevator that is accelerating upwards. The force exerted by the elevator on the person is the normal force, represented by N. The force due to gravity acting on the person is the weight, represented by mg, where m is the mass of the person and g is the acceleration due to gravity.
When the elevator accelerates upwards, it creates an additional upward force that counteracts the force due to gravity. This additional force is exerted by the floor of the elevator and is equal in magnitude and opposite in direction to the force due to gravity. This additional force is the normal force, N.
Therefore, in this case, the normal force N is equal to the force due to gravity mg, resulting in N = mg.
The correct answer in this case is actually b) N = mg. Let me explain the reason behind it.
When a person is standing in an elevator that is accelerating upwards, there are two forces acting on the person: the force due to gravity (mg), and the normal force (N) exerted by the elevator floor on the person.
Gravity always acts downwards and has a magnitude equal to the person's weight, which is mass (m) multiplied by the acceleration due to gravity (g).
The normal force, on the other hand, is the force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is exerted by the elevator floor to support the person.
When the elevator is stationary or moving at a constant velocity (not accelerating), the gravitational force (mg) and the normal force (N) balance each other out, resulting in the normal force being equal to the person's weight (N = mg). This is because the person's weight is exactly counteracted by the normal force, resulting in a net force of zero.
However, when the elevator starts accelerating upwards, the normal force needs to increase to provide an additional upward force to the person. In this situation, the normal force becomes greater than the person's weight (N > mg) to produce a net upward force on the person.
It's important to note that if the elevator were accelerating downwards or even at a constant velocity, the normal force would be less than the person's weight (N < mg). But since the elevator is accelerating upwards, the normal force must be greater than the person's weight to create an upward net force on the person.
So, in summary, the correct relationship between the force due to gravity (mg) and the normal force (N) when a person is standing in an elevator that is accelerating upwards is N = mg.