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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 80 kg, are pulled at a constant speed by a tow rope that maintains a constant tension of 360 N. How much thermal energy is created in the slope and the tube during the ascent of a 30-m-high, 120-m-long slope?

Respuesta :

Answer:

[tex]E_{th} = 19680 J[/tex]

Explanation:

GIVEN DATA:

Total mass ( rider  + his tube) = 80 kg

tension  Force = 360 N

height of slope  =  30 m

length of slope = 120 m

we know that thermal energy is given as

E_{th}  = W- Ug

W= F*d = (360N*120m)= 43200 J        

Ug= m*g*h = (80kg*9.8m/s2*30m) = 23520 J

[tex]E_{th} = 43200J - 23520 J[/tex]

[tex]E_{th} = 19680 J[/tex]

Lanuel

The amount of thermal energy that is created in the slope and the tube during the ascent is 19680 Joules.

Given the following data:

  • Total mass = 80 kg
  • Tension = 360 Newton
  • Height = 30 meters
  • Displacement = 120 meters

To find the amount of thermal energy that is created in the slope and the tube during the ascent:

By applying the Law of Conservation of Energy:

[tex]Work\;done = K.E + P.E + T.E[/tex]

Where:

  • K.E is the kinetic energy.
  • P.E is the potential energy.
  • T.E is the thermal energy.

Since the rider and his tube are pulled at a constant speed, K.E is equal to zero (0).

Therefore, the formula now becomes:

[tex]Work\;done = 0 + P.E + T.E\\\\T.E = Work\;done-P.E[/tex]

For the work done:

[tex]Work\;done = Tensional\;force \times displacement\\\\Work\;done = 360 \times 120[/tex]

Work done = 43,200 Joules.

For P.E:

[tex]P.E = mgh\\\\P.E = 80\times9.8\times30[/tex]

P.E = 23,520 Joules.

Now, we can find the amount of thermal energy:

[tex]T.E = Work\;done-P.E\\\\T.E =43200-23520[/tex]

T.E = 19680 Joules.

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