How to Calculate Magnitude of Force Applied in an Elevator

What is the magnitude of force that must be applied in the elevator scenario?

If the coefficient of kinetic friction between the box and elevator floor is 0.35, what magnitude of force must you apply?

Answer:

The magnitude of force that must be applied is 80.1 N.

When you are riding in an elevator on the way to the eighteenth floor of your dormitory, and its upward acceleration is 1.91 m/s2, and beside you is a box containing your new computer with a total mass of 29.0 kg, you need to calculate the magnitude of force required.

The force applied on the box should be equal to the frictional force of the elevator floor on the box. This can be represented by the equation F = μR, where F is the force applied, μ is the coefficient of kinetic friction, and R is the normal reaction.

Since the elevator is moving upward with a constant acceleration, the weight of the box and its contents can be calculated as W = m(g + a), where m is the mass, g is the acceleration due to gravity, and a is the upward acceleration of the elevator.

After calculating the weight and normal reaction, you can then substitute the values into the equation F = μR to find the magnitude of force that must be applied, which is 80.1 N in this scenario.