Suppose two tugboats push on a barge at different angles, as shown in Figure 4.21. The first tugboat exerts a force of 2.7 x 10⁵ N in the x-direction, and the second tugboat exerts a force of 3.6 x 10⁵ N in the y-direction.

If the mass of the barge is 5.0 x 10⁶ kg and its acceleration is observed to be 7.5 x 10^-2 m/s² in the direction shown, what is the drag force of the water on the barge resisting the motion? (Note: drag force is a frictional force exerted by fluids, such as air or water. The drag force opposes the motion of the object.)

Strategy

The directions and magnitudes of acceleration and the applied forces are given in Figure 4.21(a). We will define the total force of the tugboats on the barge as F_app so that:

Since the barge is flat bottomed, the drag of the water F_D will be in the direction opposite to F_app, as shown in the free-body diagram in Figure 4.21(b). The system of interest here is the barge, since the forces on it are given as well as its acceleration. Our strategy is to find the magnitude and direction of the net applied force F_app, and then apply Newton's second law to solve for the drag force F_D.

Transcribed Image Text:

F, 2.7 x 105 N (a) 53.1° Fy = 3.6 x 105 N F₁ /Fo F₁ Fnet F₁ Fo (b) F₂ 53.1° app F, YA