Question

directions: solve the problems shown below. any data, calculations, or models you use to support your thinking should be explained. base your answers to the following three questions on the information provided below. image of stacks of boxes with masses m, 2m, 4m the stacks of boxes shown in the figure above are inside an elevator that is moving upward. the masses of the boxes are given in terms of the mass m of the lightest box. 1. assume the elevator has upward acceleration a, and consider the stack that has two boxes of mass m. what is the magnitude of the force exerted on the top box by the bottom box? a. mg b. ma c. m(a - g) d. m(a + g)

Explanation:

Step1: Identify forces on top box

The top box has mass \( M \). Forces acting on it: gravitational force \( F_g = Mg \) (downward) and normal force \( F_N \) (upward, from bottom box).

Step2: Apply Newton's second law

Newton's second law: \( F_{net} = ma \). Net force on top box: \( F_N - Mg = Ma \) (since acceleration \( a \) is upward, net force is upward).

Step3: Solve for \( F_N \)

Rearrange the equation: \( F_N = M(a + g) \). This is the force exerted by bottom box on top box.

Answer:

d. \( M(a + g) \)