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 84 kg , are pulled at a constant speed by a tow rope that maintains a constant tension of 350 N .

Answer 1

Answer:

17304 J

Explanation:

Complete statement of the question is :

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 84 kg , are pulled at a constant speed by a tow rope that maintains a constant tension of 350 N .

Part A

How much thermal energy is created in the slope and the tube during the ascent of a 30-m-high, 120-m-long slope?

Solution :

$T$ = tension force in the tow rope = 350 N

$L$  = length of the incline surface = 120 m

$W_{t}$  = work done by tension force = ?

The tension force acts parallel to incline surface, hence work done by tension force is given as

$W_{t} = T L\\W_{t} = (350) (120)\\W_{t} = 42000 J$

$h$ = height gained by the rider = 30 m

$m$ = total mass of rider and tube = 84 kg

Potential energy gained is given as

$U = mgh\\U = (84) (9.8) (30)\\U = 24696 J$

$Q$  = Thermal energy created

Using conservation of energy

$Q = W_{t} - U\\Q = 42000 - 24696\\Q = 17304 J$