Two crates ( m 1 is known; m 2 is unknown) are being dragged together (one linke

Question

Two crates (m1 is known; m2 is unknown) are being dragged together (one linked to the other via a horizontal cable, as shown) across the floor of a large freight elevator. The crates

Two crates (m1 is known; m2 is unknown) are being dragged together (one linked to the other via a horizontal cable, as shown) across the floor of a large freight elevator. The crates' horizontal velocity is constant. The elevator is accelerating upward at a known rate, a. The pulling force F is known, as is the angle q above the horizontal at which F pulls. The coefficient of kinetic friction, mK, between each crate and the elevator floor is also known. Find m2, expressed in terms of m1, a, F, mK and g.

Explanation / Answer

The downward acceleration will be (g+a)

Equation for mass m1 :

F cos x - (m1(g+a) - F sin x)mk - T = 0

x is theta.

Net Force is zero. So acceleration a is 0.

Equation for mass m2:

T - mk m2(g + a) = 0

Adding the 2 equations , we get :

F cos x - (m1(g+a) - F sin x )mk = mk m2(g + a)

m2 = [F cos x - (m1(g+a) - F sin x )mk ]/[mk( g + a)]

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