Question

A new ride being built at an amusement park includes a vertical drop of 126.5 meters. Starting from rest, the ride vertically drops that distance before the track curves forward. If the velocity at the bottom of the drop is 10.0 m/s and the mass of the cart and passengers is 3.5 x 104 kg, how much potential energy was converted into thermal energy (heat)

Answer 1

The energies which is converted into thermal energy  is

2280.9 ×  10^4 J

According to the question when the ride will go upward then there will a potential energy acquired and when it comes down then kinetic energy starts to increase. since, the ride is starting from rest then kinetic energy will be maximum at lowest. So, now we will calculate P.E and K.E at various points.

Potential Energy at top when the vertical drop is 126.5 m is given as- P.E = m ×g× h

= 3.5 × 10^4 × 9.8 × 126.5

= 4338.95 × 10^4 J

Kinetic Energy at bottom when ride has velocity of 10 m/s then it is

given as -

K.E = 1/2 mv²

= 1/2 × 3.5×10^4 × 10²

= 175 × 10^4 J

Now the energy which converted to thermal energy is given as:

Thermal energy =  Potential energy - kinetic energy

= 2455.9 × 10^4 - 175 × 10^4

= 2280.9 × 10^4 J

Thus, the ride Potential energy was converted to thermal energy is 2280.9 × 10^4 J.  

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