Question

In the winter activity of tubing, riders slide down snow covered slopes while sitting on large inflated rubber tubes. To get to the top of the slope, a rider and his tube, with a total mass of 88 kgkg , are pulled at a constant speed by a tow rope that maintains a constant tension of 350 NN .
How much thermal energy is created in the slope and the tube during the ascent of a 30-m-high, 120-m-long slope?

Answer 1

Answer:

16.10 kJ

Explanation:

The thermal energy created in the slope can be found by definition of work (W):  

$W = E_{f} - E_{i} = K_{f} + P_{f} + Th_{f} - (K_{i} + Th_{i})$

Where:

$K_{f}$ and $K_{i}$: is the final and initial kinetic energy

$P_{f}$: is the final potential energy

$Th_{f}$ and $Th_{i}$: is the final and initial thermal energy

$W = \frac{1}{2}mv_{f}^{2} + mgh - \frac{1}{2}mv_{i}^{2} + Th_{f} - Th_{i}$

We have that W is:

$W = F*d = T*d$

Where:

F: is the force equal to the tension (T)

d: is the displacement = 120 m

And since the speed is constant, $v_{i}$ = $v_{f}$ we have:

$T*d = mgh + \Delta Th$

$\Delta Th = T*d - mgh = 350 N*120 m - 88 kg*9.81 m/s^{2}*30 m = 16101.6 J$

Therefore, the thermal energy created in the slope and the tube during the ascent is 16.10 kJ.

I hope it helps you!