The mechanism for a gumball machine is shown in Fig. 1 and 2. To begin dispensin

Question

The mechanism for a gumball machine is shown in Fig. 1 and 2. To begin dispensing a gumball, as shown in Fig. 1, a horizontal force P_1 is applied to block A to cause it to begin sliding to the right while member CD simultaneously begins to lift door B. After the door B is fully open, as shown in Fig. 2, the gumball drops out of the machine. Blocks and B weigh 0.4 lb and 0.2 lb, respectively, and the weights of member CD and the gumballs may be neglected. The pins at points C and D are frictionless, blocks A and B are a loose fit in their tracks, and all contact surfaces have a coefficient of friction of 0.4. The motion of the blocks is slow enough so that static equilibrium may be assumed. Determine the value of P_1 that will cause block A to begin moving to the right.

Explanation / Answer

The horizontal force is required to overcome the following

1. the friction against it offered by the blockA in moving distance d1 = m1 x g x mu x d1

2. the force required to lift the block B through a distance d2 = m2 x g x d2

3. The frictional force offered by block B = m2 g x mu x d2

So P1 = 0.4/2.2 x 9.8 x (4-1.4) x 0.4 x 1/100 + 0.2 /2.2 x 9.8 x (4.8 - 3)/100 + 0.2 /2.2 x 0.4 x 1.8/100 ...........0.02 N..Ans

(The numbers have been converted to uniform kg and m unit from the mixed up lb and cm system)

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