Three people push on a box from different sides and with varying strengths. (See

Question

Three people push on a box from different sides and with varying strengths. (See Fig. 2) Determine the resulting acceleration of the box. Comments An illustration of the contrived system is provided in Fig. 2. The mass of the box is m = 10 kg. The magnitude and direction of each force is specified in the figure. You can use Newton's Second Law F = ma to determine the acceleration. Recall that we may equate the x component of the left hand side of this equation to the x component of the right hand side. We may do the same for the y components. FIG. 2: Sketch of the system described in Problem 2. A box of mass m = 10 kg is pushed by three forces. You are asked to determine the acceleration of the box.

Explanation / Answer

Net magnitude of force in x-direction

Fx =(6-8)ex =-2Nex

Net magnitude of force in y-direction

Fy = 10 Ney

Net force on the box

F=sqrt[(-2)2+102] =10.2 N

acceleration of the box

a=F/m =10.2/10 =1.02 N

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