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

16.10 kJ

Step-by-step 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 = (1)/(2)mv_(f)^(2) + mgh - (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!