A tugboat exacts a constant force of 5 000N on a ship moving at constant speed through a harbor. How much work does the tugboat do on the ship in a distance of 3.00 km?
5,000 * 3,000 Joules
15 million Joules
To find the work done by the tugboat on the ship, we can use the formula:
Work = Force x Distance x Cosine(theta)
Where:
- Force is the magnitude of the force exerted by the tugboat (5,000 N).
- Distance is the distance over which the force is exerted (3.00 km).
- Cosine(theta) is the cosine of the angle between the force and the direction of motion. Since the tugboat is applying a force in the direction of the ship's motion, the angle is 0 degrees, and the cosine of 0 degrees is 1.
Plugging in the values:
Work = 5,000 N x 3.00 km x Cosine(0 degrees)
Since Cosine(0 degrees) is equal to 1, the equation simplifies to:
Work = 5,000 N x 3.00 km x 1
Now, we can calculate the work:
Work = 15,000 N * km
To convert km to meters, we multiply by 1,000:
Work = 15,000 N * 3,000 m
This gives us:
Work = 45,000,000 N * m
Therefore, the tugboat does 45,000,000 joules of work on the ship.
To find the work done by the tugboat on the ship, we can use the formula:
Work = Force x Distance x Cos(θ)
Where:
- Work is the amount of energy transferred or mechanical energy done on an object, measured in joules (J)
- Force is the applied force, measured in newtons (N)
- Distance is the distance over which the force is applied, measured in meters (m)
- θ (theta) is the angle between the applied force and the direction of motion of the object
In this case, since the tugboat is exerting a constant force in the direction of motion of the ship, the angle (θ) between the force and direction of motion is 0 degrees. Therefore, the cosine of 0 degrees is 1.
Substituting the given values into the formula:
Force = 5,000 N
Distance = 3.00 km = 3,000 m
θ = 0 degrees
Work = 5,000 N x 3,000 m x Cos(0)
= 15,000,000 J
Therefore, the tugboat does 15,000,000 joules of work on the ship as it moves through the harbor.