One boat tows another boat by means of a tow line, which is under a constant tension of 495 N. The boats move at a constant speed of 4.75 m/s. How much work is done by the tension in 1.10 min?
Not sure how to apply the work-energy theorem. I assume velocity needs to be calculated from given speed and change in distance.
You do not have to calculate velocity. They tell you what it is.
Work = (towing force) x (distance)
Distance = 4.75 m/s * 66 seconds = 313.5 m
Put it all together
To apply the work-energy theorem in this situation, you don't need to calculate the velocity of the boat. Instead, you can directly use the given speed, tension, and time to find the work done.
The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done by the tension in the tow line is equal to the change in kinetic energy of the boat being towed.
The formula for calculating work is:
Work = Force * Distance * cos(theta)
where theta is the angle between the force and the direction of motion (which is 0 degrees in this case since the force and motion are in the same direction).
Since the boats move at a constant speed, there is no change in kinetic energy. This means that the work done by the tension in the tow line is zero.
Therefore, no work is done by the tension in 1.10 minutes.
To apply the work-energy theorem in this scenario, we need to calculate the work done by the tension in the tow line. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
In this case, the work done by the tension in the tow line can be calculated using the formula:
Work = Force * Distance * cos(theta)
Where:
- Force is the constant tension in the tow line (495 N).
- Distance is the change in distance covered by the boats.
- theta is the angle between the force vector and the direction of motion (which is 0 degrees in this case since the boats move in the same direction as the force).
To calculate the distance covered by the boats, we can use the formula:
Distance = Velocity * Time
Where:
- Velocity is the constant speed of the boats (4.75 m/s).
- Time is given as 1.10 min. However, we need to convert it to seconds, as the SI unit for time is seconds.
1.10 min = 1.10 * 60 s = 66 s
So, the distance covered by the boats is:
Distance = 4.75 m/s * 66 s = 313.5 m
Now, we can plug these values into the work formula:
Work = 495 N * 313.5 m * cos(0) = 155,017.5 joules
Therefore, the work done by the tension in 1.10 min is 155,017.5 joules.