Assume the mass of the cart is 828 g, and there is no friction anywhere Suppose

Question

Assume the mass of the cart is 828 g, and there is no friction anywhere

Suppose that the graph of force vs. time for a very unusual spring has only straight lines. The cart hits the spring at t = 3.00 s, so force F = 0 up to that point. Then, after  t = 3.00 s, the force increases linearly until it reaches a maximum at Fmax = 3.29 N at time t = 3.97s. Then the spring pushes the cart away, and the force decreases linearly until it goes back to F = 0 at time t = 4.32 s.

a) Find the magnitude of the impulse exerted by the spring on the cart.
J = __ N-s

b) Find the speed of the cart just as it leaves the spring.
HINT: Assume the cart is at rest when the force exerted by the spring is a maximum.
v = __ m/s

c) For the graph described above: what does this graph tell you about the initial speed of the cart vo and the final speed of the cart vf

vo must be greater than vf

vo must be less than vf     

You cannot tell if vo is greater than or less than vf

vo must be equal than vf

Explanation / Answer

a)

J = area under the graph

J = (1/2)*Fmax*(t1-t) + (1/2)*Fmax*(t2-t1)

J = (0.5*3.29*(3.97-3)) + (0.5*3.29*(4.32-3.97))

J = 2.1714 Ns

(b)

change in momentum from maximum compression to the point as it leaves the sping

m*vf = impulse = 0.5*Fmax*(t2-t1)

0.828*v = 0.5*3.29*(4.32-3.97)

vf = 0.69 m/s

+++++++++++++

(c)

for the first half

m*vo = 0.5*Fmax*(t1-t)

0.828*vo = 0.5*3.27*(3.97-3)

vo = 1.92 m/s

vo must be greater than vf

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