Three people push on a box from different sides and with var

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.

Solution

Net magnitude of force in x-direction

F_x =(6-8)e_x =-2Ne_x

Net magnitude of force in y-direction

F_y = 10 Ne_y

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