Question

1) A block of mass m = 0.52 kg is attached to a spring with force constant 119 N/m is free to move on a frictionless, horizontal surface as in the figure below. The block is released from rest after the spring is stretched a distance A = 0.13 m. (Indicate the direction with the sign of your answer. Assume that the positive direction is to the right.)

(a) At that instant, find the force on the block.   N   (b) At that instant, find its acceleration.    m/s²

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2) A 10.0-g bullet is fired into, and embeds itself in, a 1.80-kg block attached to a spring with a force constant of 22.4 N/m and whose mass is negligible. How far is the spring compressed if the bullet has a speed of 300 m/s just before it strikes the block and the block slides on a frictionless surface? Note: You must use conservation of momentum in this problem because of the inelastic collision between the bullet and block. ___ m

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3) A horizontal object-spring system oscillates with an amplitude of 2.8 cm. If the spring constant is 280 N/m and object has a mass of 0.50 kg, determine each of the following values.
(a) the mechanical energy of the system J (b) the maximum speed of the object   m/s (c) the maximum acceleration of the object    m/s²

Answer 1

1)

(a) By F = -kx

=>F = -119 x 0.13 = -15.47 N [-ve is just indicating the direction of Force]

(b) By a(x) = - ω^2x

=>a(x) = -(2πn)^2x

=>a(x) = -(2π x 1/2π√[k/m])^2x

=>a(x) = -(k/m)x

=>a(x) = -(119 x 0.13)/0.52

=>a(x) = -29.75 m/s^2 [-ve indicating that it is retardation]