Work Done on Sled by Rope in 15s: kJ Answer

[natedebar72]

I need help on total work...

2. [GRR1 6.P.002.] A sled is dragged along a horizontal path at a constant speed of 1.5 m/s by a rope that is inclined at an angle of 30.0° with respect to the horizontal (the figure below). The total weight of the sled is 470 N. The tension in the rope is 230 N. How much work is done by the rope on the sled in a time interval of 15.0 s?
I need the answer in kJ

 

[marlon]

What have you done so far ?
Show us your calculations.

What's the formula you apply in order to calculate the work ? What two quantities do you need to know in order to be able to apply this formula.

HINT one of the quantities has been given, you need to calculate the other one yourself.

marlon

 

[kyle8921]

To calculate the work done by the rope on the sled, we can use the formula W = Fdcosθ, where F is the force applied, d is the displacement, and θ is the angle between the force and displacement vectors.

In this case, the force applied by the rope is the tension, which is 230 N. The displacement of the sled is the distance it travels in 15 seconds, which can be calculated using the speed of 1.5 m/s and the time of 15 seconds. This gives us a displacement of 22.5 m.

The angle between the force and displacement vectors is 30.0°, so we can plug all these values into the formula to get:

W = (230 N)(22.5 m)(cos 30.0°)
W = 3,937.5 Nm

To convert this to kJ, we need to divide by 1000 to get the work in Joules, and then divide by 1000 again to get the work in kJ. This gives us a final answer of 3.94 kJ.

Therefore, the work done by the rope on the sled in 15 seconds is 3.94 kJ.