A 1000-kg barge is being towed by means of two horizontal cables. One cable is pulling with a force of 80.0 N in a direction 30.0° west of north. The second cable pulls in a direction 20.0° east of north. What should the magnitude of its pulling force be so that the barge will accelerate northward?
A) 127 N
B) 120 N
C) 117 N
D) 73.7 N
E) 58.5 N

Question

Quizplus · Accepted Answer

To ensure the barge accelerates northward, the east-west components of the forces must cancel out. The westward component of the 80.0 N force is 80.0 N * sin(30°) = 40.0 N. The eastward component of the second force must also be 40.0 N to cancel it out. If F is the magnitude of the second force, then F * sin(20°) = 40.0 N. Solving for F gives F = 40.0 N / sin(20°) ≈ 117 N.

A 1000-Kg Barge Is Being Towed by Means of Two