Answer to Question #192050 in Mechanics | Relativity for Nicole

Question

Two boxes, mass M and 3M are stacked on top of each other. The stack of boxes is placed inside an elevator which is accelerating upwards.

When the elevator accelerates upward with an acceleration equal to a, which of the following will correctly give the magnitude of the force which the bottom box applies to the top box?

(A) 3Mg

(B) 3Ma

(C) 3M(a-g)

(D) 3M(a+g)

Answer 1

Explanations & Calculations

• Assume the reaction force on the topmost box $\small (3M)$ from the other one $\small (M)$ is $\small R$ during the motion.
• Then if we consider the topmost box only, we see its own weight $\small 3Mg\downarrow$ and the said reaction force $\small R \uparrow$ as the only forces to act on it during the motion.
• And we are told that those two boxes accelerate at a.
• Then it is about applying Newton's second law on this box along the moving direction $\uparrow$.

$\qquad\qquad \begin{aligned} \small \uparrow F&=\small ma\\ \small R-3Mg&=\small 3Ma\\ \small R&=\small 3Mg+3Ma\\ &=\small 3M(g+a) \end{aligned}$

• The force on it is increased beyond its weight & this is obvious as this reaction force should support the mass while giving it that much acceleration at the same time.