Question

A cardboard box rests on the floor of an elevator. The box has a mass m = 4.75 kg and the elevator has an upward acceleration of a.

If the elevator's acceleration has a magnitude of g in the downward direction, what would the normal force, Fₙ₁ be in Newtons?
If the elevator's acceleration had a magnitude of g in the upward direction, what would the normal force Fₙ₂ be in Newtons?

Answer 1

The normal force when the elevator accelerates downwards at g is 0 Newtons since the acceleration cancels out gravity, and 93.2 Newtons when the elevator accelerates upwards at the same magnitude of g, as the normal force adds to the gravitational force.

Step-by-step explanation:

The normal force on the box can be found using Newton's Second Law of Motion, which states that the force on an object is equal to its mass (m) multiplied by its acceleration (a). In the case of the box in the elevator, the acceleration due to gravity (g) will affect the normal force differently depending on the direction of the elevator's acceleration.

When the elevator accelerates downwards with acceleration a of magnitude g, the normal force (Fn1) would be:

Fn1 = m * (g - a) = m * (g - g) = m * 0 = 0 Newtons

When the elevator accelerates upwards with the same magnitude g, the normal force (Fn2) would be:

Fn2 = m * (g + a) = 4.75 kg * (9.8 m/s2 + 9.8 m/s2) = 4.75 kg * 19.6 m/s2 = 93.2 Newtons

The normal force acts in the upward direction in both cases, opposing the direction of weight.