Question

1. Determine the range of force P that yields the equilibrium of the two-block system shown in the figure. Assume that friction exists only at the bottom surface of B. figure. Assume that 3001 58N 534 N B 356 N My = 0.2-

Answer 1

In the given state of the problem, block A pushes block B downwards as well as towards the left. When P is maximum (keeping the system in equilibrium), block B is just about to move towards the right. And as friction opposes the motion, it will act towards left (as shown in Figure 1, in image 2). When P is minimum (keeping the system in equilibrium), block B is just about to move towards the left and thus friction force acts towards the right (as shown in Figure 2 in image 2).

Applying the equilibrium equations ($\sum$F_x=0 and $\sum$ F_y=0) we can find the required values.

Ans. The range of force P that yields the equilibrium of the two-block system is 130.305 N to 486.305 N.

In the gisten state of problem, block A (weight of block A) Rushes black B downwards as well as towards the left. When p is mascimum ( keeping the system in equilibrium), the block B is just about to move towards the right. And as friction opposes motion, the friction force will act towards the left. You can refer figure ! when p is minimum (keeping the sustem in equillibrium) the block B is just about to move towards the left. And as friction opposes motion, the friction force will act towards the right. You can refer figure 2.

N, Sin30 - N, Sinzok 73 EN N, 20030 IN 2000 VN 4534N N, 0030 > √356N 356N N, Sin30 N Fig. 3 FBO of block A Fig. 1 FBD of block B when P is maximum. (friction force of acts towards left Fig. 2 FBO of blocks when P is minimum (friction force of acts towards right)

From figure 3, Apply Efy =o, N, Cos 30 = 534 N, = 616.61N In both cases (Pmase and Prin), N = 356+ N, Cos30 = 356 + 534 N = 8 ION ( from figure I and 2, applying & Fy=0)

Now, In figure , and figure 2, friction force, f = UN = 0.28 890 t = 178N In figure I applying e Forzo Pmax = f + N, sin 30 = 178 + 616.61 Sinzo I Pmax = 486.305 N In figure 2 applying EFx To => Pmin = N Sin 3o - f = 616.61 Sino - 178= 130.305 N Pmin = 130.305N

Ars. The range of force p that yeilds the equilibrium of the two block system is Poris = 130-305 N to Pmas = 486.305N no