Question

Two blocks, each with weight w, are held in place on a frictionless incline as shown below. In
terms of w and the angle of the incline, calculate the tension in (a) the rope connecting the blocks and (b) the rope that connects block A to the wall. (c) Calculate the magnitude of the force that the incline exerts on each block. (d) Interpret your answers for the cases in which the angles are 0 degrees & 90 degrees

Answer 1

a)

$$T_1=m_Bg\sin{\alpha}=W\sin{\alpha}$$

b)

$$T_2=T_1+m_Ag\sin{\alpha}=W\sin{\alpha}+W\sin{\alpha}\\=2W\sin{\alpha}$$

c)

$$R_A=m_Ag\cos{\alpha}=W\cos{\alpha}$$

$$R_B=m_Bg\cos{\alpha}=W\cos{\alpha}$$

d) 1) $\alpha=0\degree$

$$T_1=T_2=0\ N$$

$$R_A=R_B=W$$

We have two blocks on horizontal plane, no forces between them.

2) $\alpha=90\degree$

$$R_A=R_B=0\ N$$

$$T_1=W, T_2=2W$$

Both blocks are hanging in the air.