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 to move the tanker?
10o W. of N. = 100o CCW.
10o E. of N. = 80o CCW.
Fr = 1.8*10^6[100o] + 1.8*10^6[80o]=-3.126*10^5+1.773*10^5i + 3.126^10^5+1.773*10^5i = 3.546*10^5i = 3.546*10^5[90o] = 3.546*10^5N., Due North. = Resultant force.
Work = Fr*d = 3.546*10^5 * 500 =
To find the total work done by the tugboats to move the tanker, we need to calculate the work done by each tugboat and then add them together.
1. First, let's calculate the work done by the tugboat pulling at 10° west of North. The force exerted by this tugboat is 1.8x10^6 N. However, this force is not directly in the direction of motion (north), so we need to find the component of the force that is acting in the north direction.
To find the northward component of the force, we can multiply the force by the cosine of the angle between the force and the north direction. Since the angle is given as 10° west of North, the angle between the force and the north direction is 10°.
Northward force = Force * cos(angle) = 1.8x10^6 N * cos(10°)
2. Next, let's calculate the work done by the tugboat pulling at 10° east of north. Similar to the previous step, we need to find the component of the force in the north direction.
To find the northward component of the force, we can multiply the force by the cosine of the angle between the force and the north direction. Since the angle is given as 10° east of North, the angle between the force and the north direction is 10°.
Northward force = Force * cos(angle) = 1.8x10^6 N * cos(10°)
3. Now, we can calculate the work done by each tugboat using the formula:
Work = Force * Distance
The distance traveled by the tanker is given as 0.50 km.
Work done by the tugboat pulling at 10° west of North = Northward force * Distance
Work done by the tugboat pulling at 10° east of North = Northward force * Distance
4. Finally, we can calculate the total work done by adding the work done by each tugboat:
Total work done = Work done by the tugboat pulling at 10° west of North + Work done by the tugboat pulling at 10° east of North
Please note that throughout this calculation, angles and trigonometric functions are used to determine the components of the forces in the north direction.