Question

In a tug-of-war game on one campus, 15 students pull on a rope at both ends in an effort to displace the central knot to one side or the other. Two students pull with force 196 N each to the right, four students pull with force 98 N each to the left, five students pull with force 62 N each to the left, three students pull with force 150 N each to the right, and one student pulls with force 250 N to the left. Assuming the positive direction to the right, express the net pull on the knot in terms of the unit vector. How big is the net pull on the knot? In what direction?

a) ( -4.6 , {N} , hat{i} ); left
b) ( 4.6 , {N} , hat{i} ); right
c) ( -3.2 , {N} , hat{i} ); left
d) ( 3.2 , {N} , hat{i} ); right

Answer 1

The net pull on the knot is to the left with a magnitude of 110 N, which is expressed as (-110, {N}, hat{i}); left.

Step-by-step explanation:

To determine the net pull on the knot in the tug-of-war game, we need to calculate the total force exerted to the right and to the left, and then find the difference between them.

• Right: 2 students × 196 N + 3 students × 150 N = 392 N + 450 N = 842 N
• Left: 4 students × 98 N + 5 students × 62 N + 1 student × 250 N = 392 N + 310 N + 250 N = 952 N

The net force exerted is the total force to the right minus the total force to the left, which is 842 N - 952 N = -110 N. A negative value indicates that the net pull is to the left, with a magnitude of 110 N.

Expressing the force in vector form with the positive direction as the right, we can write:

(-110 N) ⋅ {N} ⋅ hat{i} which translates into option (a) (-110, {N}, hat{i}); left.