m 1 = 13 kg m 2 = 23 kg, (a) Determine the height h from which cart 1 would need

Question

m1 = 13 kg m2 = 23 kg,     (a) Determine the height h from which cart 1 would need to start to make sure that cart 2 completes the loop without leaving the track. Assume an elastic collision.
1             m

    (b) Find the height needed if instead the more massive cart is allowed to slide down the ramp into the smaller cart.
2           m A cart of mass m1 = 13 kg slides down a frictionless ramp and is made to collide with a second cart of mass m2 = 23 kg, which then heads into a vertical loop of radius 0.26 m as shown in the figure below.

Explanation / Answer

Velocity required to complete the circle =sqrt(5rg)

=3.57m/s

part a)

Let the velocity of Cart 1 before collision is u.

Hence using energy conservation and momentum conservation

v2=2m1/(m1+m2) x u

u=4.94 m/s

Now again applying energy conservation

mgh=1/2mv^2

h=1.246m

Part b)

Let the velocity of Cart 2 before collision= u

again

v2=2m2/(m1+m2) x u

u=2.79m/s

hence

m2gh=1/2 mv^2

h=0.397 m

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