Answer to Question #262227 in Physics for Mex

Question

Figure a side shows a box of mass m2 = 1.0 kg on a frictionless plane inclined at angle ©= 30°. It is connected by a cord of negligible mass to a box of mass ml = 3.0 kg on a horizontal frictionless surface. The pulley is frictionless and massless.

If the magnitude of horizontal force is 2.3 N.

what is the tension in the connecting cord?

What is the largest value the magnitude of may have without the cord becoming

slack?

Answer 1

Determine tension with 2.3 N force:

$$m_1:T+F=m_1a,\\ m_2:-T+m_2g\sin\theta=m_2a,\\ T=3.1\text{ N},\\ a=1.8\text{ m/s}^2.$$

The maximum magnitude of the force can be found from the following condition: $T=0$. The equations:

$$m_1:0+F=m_1a,\\ m_2:-0+m_2g\sin\theta=m_2a,\\ a=4.9\text{ m/s}^2.\\F=14.7\text{ N}.$$