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 82 kg, are pulled at a constant speed by a tow rope that maintains a constant tension of 310 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?

K = 2 10⁻⁸ J

Explanation:

Let's solve this exercise in parts, we start by finding the charge on each plate of the capacitor

          C = Q / ΔV

           C = ε₀ A / d

          ε₀ A / d = Q / ΔV

          Q = ε₀ A ΔV / d        (1)

indicate the potential difference ΔV₁ = 12 V, the distance between the plates d₁ = 3 mm = 0.003 m,  

as the power supply is disconnected and the capacitor is ideal the charge remains constant

in the second part we separate the plates at d₂ = 5 mm = 0.005 m, using equation 1

          ΔV₂ =

we substitute the equation for Q

         ΔV₂ =

         ΔV₂ =

in the third part we use the concepts of energy

starting point. Test charge near positive plate

          Em₀ = U = q ΔV₂

final point. Test charge near negative plate

          Em_f = K

energy is conserved

          Em₀ = Em_f

          q ΔV₂ = K

          K = q ΔV₁

we calculate

          K = 1 10⁻⁹  12  0.005/0.003

          K = 2 10⁻⁸ J