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 955 N/m . (Ignore air resistance and any energy lost when the block initially contacts the spring.) (Figure 1) a. Suppose the mass of the block is 1.65 kg , but its initial speed can be varied. What initial speed is required to give a maximum spring compression of 3.90 cm ? b. Suppose the initial speed of the block is 1.39 m/s , but its mass can be varied. What mass is required to give a maximum spring compression of 3.90 cm ?

Explanation / Answer

k = 955 N/m
(a)
m = 1.65 kg
x = 3.90 * 10^-2 m
Let speed be v.
Using Energy Conservation,
Initial kinetic Energy = Final Stored Potential Energy
1/2 * m*v^2 = 1/2*k*x^2
1/2 * 1.65 * v^2 = 1/2 * 955 * (3.90 * 10^-2)^2
v = 0.938 m/s

(b)
Let the mass be m.
Again
Using Energy Conservation,
Initial kinetic Energy = Final Stored Potential Energy
1/2 * m*v^2 = 1/2*k*x^2
1/2 * m * 1.39^2 = 1/2 * 955 * (3.90 * 10^-2)^2
m = 0.75 Kg

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