Question 7.15: Figure 7-28 shows three forces applied to a trunk that moves......
Figure 7-28 shows three forces applied to a trunk that moves leftward by 3.00 m over a frictionless floor. The force magnitudes are F_1 = 5.00 N, F_2 = 9.00 N, and F_3 = 3.00 N, and the indicated angle is θ = 60.0 . During the displacement, (a) what is the net work done on the trunk by the three forces and (b) does the kinetic energy of the trunk increase or decrease?
(a) The forces are constant, so the work done by any one of them is given by W=\vec{F}\cdot \vec{d}, where \vec{d} is the displacement. Force \vec{F}_1 is in the direction of the displacement, so
W_1=F_1 d \cos \phi_1=(5.00 \,N )(3.00 \,m ) \cos 0^{\circ}=15.0\, J.
Force \vec{F}_2 makes an angle of 120° with the displacement, so
W_2=F_2 d \cos \phi_2=(9.00 \,N )(3.00 \,m ) \cos 120^{\circ}=-13.5\, J.
Force \vec{F}_3 is perpendicular to the displacement, so
W_3=F_3 d \cos \phi_3=0 \text{since} \cos 90^{\circ}=0 .
The net work done by the three forces is
W=W_1+W_2+W_3=15.0 \,J -13.5 \,J +0=+1.50 \,J.
(b) If no other forces do work on the box, its kinetic energy increases by 1.50 J during the displacement.