A water skier, moving at a speed of 8.36 m/s, is being pulled by a tow rope that makes an angle of 33.4 ° with respect to the velocity of the boat (see the drawing). The tow rope is parallel to the water. The skier is moving in the same direction as the boat. If the tension in the tow rope is 140 N, determine the work that it does in 11.0 s.
I got 14400 J, which was incorrect.
The force component along the direction of motion is what does work. That component is 140 cos33.4 = 116.9 N
Distance travelled in 11.0 s = 91.96 m
Multiply those numbers together for the work done, in joules.
I have no idea how you got 1440 J. If you had mistakenly omitted the cosine term, you still should not get that answer.
Thank you! I redid it with different numbers, and I got the problem correct. :)
To determine the work done by the tow rope, you can use the formula:
Work = Force × Distance × cos(θ)
Where:
- Work is the work done in joules (J)
- Force is the applied force in newtons (N)
- Distance is the distance over which the force is applied in meters (m)
- θ is the angle between the applied force and the direction of motion, measured in degrees
In this case, the force applied is the tension in the tow rope, which is given as 140 N. The distance over which the force is applied can be calculated by multiplying the skier's velocity by the time, as both the speed and the time are given.
Distance = Velocity × Time
Distance = 8.36 m/s × 11.0 s
Distance = 91.96 m
Now, we can substitute the values into the work formula:
Work = 140 N × 91.96 m × cos(33.4°)
Make sure to convert the angle to radians before using it in the formula:
θ (in radians) = θ (in degrees) × π / 180
θ = 33.4° × π / 180
θ = 0.5835 radians
Work = 140 N × 91.96 m × cos(0.5835)
Now, calculate the result:
Work = 140 N × 91.96 m × 0.8449
Work ≈ 10,293 J
Thus, the correct answer for the work done by the tow rope in 11.0 s is approximately 10,293 J, not 14,400 J.