Question

The total mechanical energy of the roller coaster cart below at Point A is 180,000 J. The speed of the cart at Point B is +20 m/s. Assume no energy is lost due to dissipative forces such as friction. A) What is the mass (in kg) of the roller coaster cart? B) What is the potential energy at Point A? C) What is the kinetic energy at Point A?

Answer 1

Mechanical energy (ME) = Potential energy(PE) + kinetic energy (KE)

PE = mgh

m= mass

g= gravity

h= height

KE= 1/2 m v^2

v= speed

Point B

ME = KE + PE

PE = 0 (height = 0 )

KE = 1/2 (m) v^2

180,000 = 1/2 (m) (20)^2

m = 180,000 / (1/2 (20)^2 )

m= 900 kg

Point A.

ME = 180,000 J = PEa + KE a

PEa = m g h = 900 (9.8) (20) = 176,400J

MEa = PEa + KEa

KEa = MEa - PEa = 180,000 - 176,400 J = 3,600 J

A) mass = 900 kg

B) 176,400 J

C) 3,600 J