As in procedure 1: a pair of carts sit on a frictionless track. Assume the mass

Question

As in procedure 1: a pair of carts sit on a frictionless track. Assume the mass of the larger cart is 3.65 times the mass of the small cart, In this system, however, there is a spring between the carts which can "explode", pushing on the two carts at once..
NOTE: Every velocity needs magnitude and direction (given by the sign).

a) Suppose the carts are initially at rest, and after the "explosion" the smaller cart is moving at velocity +3.5 m/s.
- Find the velocity of the larger cart.  m/s
- If the mass of the smaller cart is 4.05 kg, find the energy supplied by the spring to the carts.  J
- If the spring has spring constant k = 695 N/m, find the distance the spring was compressed before the "explosion".  m
HINT: Think conservation of energy!

b) Suppose the carts are initially moving together at constant velocity +1.37 m/s. After the "explosion", the smaller cart is moving at velocity +3.5 m/s. Find the velocity of the larger cart.
m/s

Explanation / Answer

Theimpulseon smallercartismv= 3.5 m.

The impulse on larger cart is - 3.65mV.

3.5 m. - 3.65mV. =0

V = 0.96 m/s

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Energy gained by smaller cart is 0.5 mv^2 = (0.5 * 4.05 * 3.5 * 3.5) = 24.80 J

Energy gained by larger cart is 0.5MV^2= (0.5 * 3.65 * 4.05 * 0.96 * 0.96) = 6.81 J

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Energy given by the spring = 1/2 kx^2

1/2 kx^2 = 24.8 + 6.81 = 31.61J

1/2 * 695* x^2 = 31.61

x^2 = 2.434 m^2

x = 8.27 * 10-3 m

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