Question

On a roller coaster ride the total mass of a cart - with two passengers included - is 319 kg. Peak K is at 43.6 m above the ground and peak L is at 24.4 m. At location K the speed of the cart is 16.4 m/s, and at location L it is 12.4 m/s. (The wheel mechanism on roller coaster carts always keeps the carts safely on the rail.) How much mechanical energy is lost due to friction between the two peaks?

Answer 1

The mechanical energy is lost due to friction between the two peak is 78,458.688 J

What is mechanical energy?

The mechanical energy is the sum of kinetic energy and the potential energy of an object at any instant of time.

M.E = KE +PE

Given is a roller coaster ride the total mass of a cart - with two passengers included - is 319 kg. Peak K is at 43.6 m above the ground and peak L is at 24.4 m. At location K the speed of the cart is 16.4 m/s, and at location L it is 12.4 m/s.

Total energy at peak K,

TE₁ = 1/2 mv₁² +mgh₁

Substitute the values, we get

TE₁ =  1/2 x319 x 16.4² +319 x 9.81 x 43.6

TE₁ = 179,340. 524 J

Total energy at peak L,

TE₂ = 1/2 mv₂² +mgh₂

Substitute the values, we get

TE₂ =  1/2 x319 x 12.4² +319 x 9.81 x 24.4

TE₂ = 100,881. 836 J

The mechanical energy lost is

M.E =  TE₁ -TE₂

M.E =  179,340. 524 J -  100,881. 836 J

M.E = 78,458.688 J

Thus, the mechanical energy is lost due to friction between the two peak i

Learn more about mechanical energy.

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