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Physics - Springs

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a 10.0 g bullet is fired into a 1.0 kg block initially at rest on a rough surface and connected to a spring with k = 200 N/m. Immediately following the collision the block has a speed of 2.0 m/s. The coefficient of friction between the ground and the block is 0.10.

a) If the block slides a distance x after the collision before turning around, what is the work done by friction over that distance (in terms of x)?
W = -umgx
= -(0.10)(1.0kg)(9.8m/s^2)x
= -0.98x

b) What is the mechanical energy of the block immediately following the collision?
E_f = .5mv_f^2 + .5kx^2
= .5(1kg)(2.0m/s^2) + .5(200N/m)x^2
= 2kg*m^2/s^2 + (100N/m)x^2

c) What is the mechanical energy of the block when it has reached its maximum compression distance x?

d) How does the value of mechanical energy immediately following the collision compare to the mechanical energy at the maximum compression point of the block? Be specific.

e) Calculate x.

f) What is the maximum velocity reached by the block as it returns to its unstretched position following compression?

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