Question

a student is standing in an elevator that is accelerating downward. the force that the student exerts on the floor of the elevator must be
(1) less than the weight of the student when at rest
(2) greater than the weight of the student when at rest
(3) less than the force of the floor on the student
(4) greater than the force of the floor on the student

Explanation:

Step1: Analyze forces

When the elevator accelerates downward, let the mass of the student be \(m\), the acceleration of the elevator be \(a\) (\(a>0\) downward), and the normal force from the floor on the student be \(N\). According to Newton's second law \(mg - N=ma\), so \(N = m(g - a)\). When at rest \(N_0=mg\). Since \(a>0\), \(N

Step2: Use Newton's third law

By Newton's third law, the force the student exerts on the floor \(F\) and the normal force \(N\) the floor exerts on the student are an action - reaction pair, so \(F = N\).

Answer:

1. less than the weight of the student when at rest