Two Tugboats pull a disabled supertanker. Each tugboat exerts a constant force 1.8x10^6 N, one at 10° west of North and other at 10° east of north, as they pull the tanker 0.50km towards north. The mass of the tanker is 2.20x10^8 kg. What is the total work the tugboats do on the tanker?
W = Fd = 2(1.8e6)cos10 *500
To find the total work done by the tugboats on the tanker, we can use the formula for work:
Work = Force x Distance x Cos(θ)
Where:
- Force is the magnitude of the force applied by each tugboat (1.8x10^6 N),
- Distance is the distance moved by the tanker (0.50 km = 500 m),
- Cos(θ) is the cosine of the angle between the force and displacement vectors.
Let's calculate the work done by each tugboat separately and then find the total work.
1. Work done by the tugboat pulling west of North:
- Force = 1.8x10^6 N
- Distance = 500 m
- θ = 10° (west of North)
Work₁ = Force x Distance x Cos(θ)
= (1.8x10^6 N) x (500 m) x Cos(10°)
≈ 878,570 J (rounded to the nearest whole number)
2. Work done by the tugboat pulling east of North:
- Force = 1.8x10^6 N
- Distance = 500 m
- θ = 10° (east of North)
Work₂ = Force x Distance x Cos(θ)
= (1.8x10^6 N) x (500 m) x Cos(10°)
≈ 878,570 J (rounded to the nearest whole number)
Now, to find the total work, we add the work done by each tugboat:
Total Work = Work₁ + Work₂
= (878,570 J) + (878,570 J)
≈ 1,757,140 J (rounded to the nearest whole number)
Therefore, the total work done by the tugboats on the tanker is approximately 1,757,140 Joules.