A cart of mass m 1 = 14 kg slides down a frictionless ramp and is made to collid

Question

A cart of mass m1 = 14 kg slides down a frictionless ramp and is made to collide with a second cart of mass m2 = 29 kg which then heads into a vertical loop of radius 0.21 m as shown in Figure P7.66.

(a) Determine the height h at which cart #1 would need to start from to make sure that cart #2 completes the loop without leaving the track. Assume an elastic collision.

(b) Find the height needed if instead the more massive cart is allowed to slide down the ramp into the smaller cart

Explanation / Answer

a)

the minimum speed of the cart at the top of the loop is, v = sqrt(g*r)

so apply conservation of energy

m*g*h = m*g*(2*r) + (1/2)*m*v^2

m*g*h = 2*m*g*r + (1/2)*m*(g*r)

m*g*h = (5/2)*m*g*r

h = 2.5*r

= 2.5*0.21

= 0.525 m <<<<<<<<-----------Answer

b) height does not depend on mass.

so, same height. i.e 0.525 m

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