Question

The following figure represents the ride for a cart with a mass of 200 kg along a frictionless track.



a. Calculate the velocity of the cart at points A, B, and C if the cart is dropped from a height of 100m with a initial velocity of 10 m/s.


b. Calculate the height of the second loop knowing that the velocity of the cart is 24.5 m/s.

c. Calculate the total Energy of the cart for any one of the points A through D.

Answer 1

I do not have your figure.
HOWEVER

(Note - I do not care what mass it is, call it m not 200 until part c)

initial kinetic energy = (1/2)m(100) = 50 m

Ke at any height h = 50 m + m g (100-h)
so at any height h (Points A B and C)
(1/2) m v^2 = 50 m + m g (100-h)
note m cancels)
v^2 = 2 ( 50 + 100 g - g h)
v^2 = 100 + 2g (distance fallen)

that does part a
use the same equation for part b, solve for h

Part c is a trick question
the total energy (Kinetic + potential) is the same everywhere
(1/2) m v^2 + m g h
just do it at the bottom when h = 0