IP A block slides on a horizontal, frictionless surface until it encounters a sp

Question

IP A block slides on a horizontal, frictionless surface until it encounters a spring with a force constant of 965 N/m. (Ignore air resistance and any energy lost when the block initially contacts the spring.)

Part A.

Suppose the mass of the block is 1.80 kg , but its initial speed can be varied. What initial speed is required to give a maximum spring compression of 4.00 cm ?

Part B.

Suppose the initial speed of the block is 1.19 m/s , but its mass can be varied. What mass is required to give a maximum spring compression of 4.00 cm ?

Part B.

Suppose the initial speed of the block is 1.19 m/s , but its mass can be varied. What mass is required to give a maximum spring compression of 4.00 cm ?

Explanation / Answer

A) As the system operates without friction. KE lost by block = energy (E) gained by spring

For the spring, energy stored .. E = ½ ke²
E = ½ x 965 N/m x (0.04m)² = 0.772 J (= KE that has to be transferred to spring)
KE = 0.772 = ½ mv²
v = (2 x 0.772/1.80kg) = 0.926 m/s

(B) E = 0.772 J .. as before
KE = 0.772 = ½ m (1.19m/s)²
m = 2 x 0.772/(1.19)² = 1.09 kg

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