The 100 kg roller coaster car starts starts from rest at the top of a 50 m tall hill. The car then goes down the hill and goes into a corkscrew that is 20 m tall.

Question

     a) Find the total mechanical energy at the top of the first hill. 

     b) Find the total mechanical energy in the corkscrew.

     c) Find the gravitational potential energy in the loop.

     d) Find the speed of the rollercoaster cart through the corkscrew.

Answer 1

a, The total mechanical energy is the sum of the potential energy and kinetic energy. At the top of the hill, the mechanical energy is all potential which is equal to mgh where m is the mass, g is the acceleration of gravity, and h is the height above the base of the hill. PE = 100 kg x 9.8 ms^-2 x 50 m = 4.9 x 10⁶ Joules.

b. Neglecting any energy losses, the total mechanical energy is 4.9 x 10⁶ Joules.

c. The highest gravitational potential energy is at the top of the loop which is 20 m tall. So, at that point, the PE = mgh = 100 kg x 9.8 ms^-2 x 20 m = 1.96 x 10⁴.

d. The speed of the cart through the loop depends on the position of the cart in the loop. It can be calculated using the total mechanical energy = KE + PE relation. At the top of the loop, for example, the

KE = 4.9 x 10⁶ - 1.96 x 10⁴ = 1/2 mV², so the speed = √4.88 x 10⁶ x 2 / 100 kg = 312 m/s.

Please check the math.