Question

Two tugboats pull a disabled supertanker. Each tug exerts a constant force of 1.30 * 10⁶ N, one at an angle 13.0° west of north, and the other at an angle 13.0° east of north, as they pull the tanker a distance 0.650 km toward the north.

Part A

What is the total work done by the two tugboats on the supertanker?
Express your answer in joules, to three significant figures.

Part B

What is the total work done by the two tugboats on the supertanker?
Express your answer in joules, to three significant figures.

Answer 1

Part A Answer

Work is force times distance. The tugs are pulling at an angle to north, but each is pulling in the opposite direction (with respect to the x-direction) – so the forces cancel out in the x-direction, and the only force left is acting in the y-direction. To begin, find the y-component of the force from one of the tugs and then double it:

Fy = F*cos(θ)
Fy = 1300000 * cos(13)
Fy = 1266681 N

Now double the force, since there are two tugs. The overall force is 2533362 N. Now multiply by the distance. 0.650 km is 650m:

W = FD
W = 2533362 * 650
W = 1646685409 J

Rounded to 3 significant figures, this is 1650000000 J, or 1.65 * 10^9

1.65 * 10^9

Part B Answer

Work is force times distance. The tugs are pulling at an angle to north, but each is pulling in the opposite direction (with respect to the x-direction) – so the forces cancel out in the x-direction, and the only force left is acting in the y-direction. To begin, find the y-component of the force from one of the tugs and then double it:

Fy = F*cos(θ)
Fy = 1300000 * cos(13)
Fy = 1266681 N

Now double the force, since there are two tugs. The overall force is 2533362 N. Now multiply by the distance. 0.650 km is 650m:

W = FD
W = 2533362 * 650
W = 1646685409 J

Rounded to 3 significant figures, this is 1650000000 J, or 1.65 * 10^9 J

1.65 * 10^9 J