Question

A mass m2 =25 kg sits atop a mass m1 =80kg on a platform​. The masses are at rest with respect to the platform, however, the platform is accelerating upwards at a rate, a = 2.2 m/s​ .

(a) Draw a free body diagram for the combined masses​.
(b) Find the normal force exerted on m1 by the platform​ (both magnitude and direction).
(c) Draw free body diagrams for both m​1 and m​2​
(d) Find the normal force exerted on m​2 by m​1 (both magnitude and direction).
(e) Find the normal force exerted on m​1 by m​2 (both magnitude and direction).

Answer 1

(a) See below:

(b) Y-axis looks down:

$$-N_1+m_1g+m_2g=-m_1a-m_2a,\\ N_1=(g+a)(m_1+m_2)=1260\text{ N}.$$

Sine N1 acts upward, the answer is -1260 N.

(c) See (a)

(d) Write Newton's second law for m2:

$$m_2g-N_{12}=-m_2a,\\ N_{12}=m_2(g+a)=300\text{ N}.$$

The force acts upward, the answer is -300 N.

(e) According to Newton's third law,

$$|N_{12}|=|N_{21}|,\\ N_{21}=300\text{ N}.$$