Assume the following represents an isolated system. A mass of m = 0.5 kg is held

Question

Assume the following represents an isolated system. A mass of m = 0.5 kg is held at rest on a spring with a constant of k_1 = 400 N/m, where the mass has been pushed to displace the spring 0.1 m from its equilibrium point. The mass is then released and travels across a surface for half a meter, where a frictional force of f_k = 1.2 N acts on the mass. The mass encounters a second spring and displaces that spring 0.2 m from its equilibrium point, before instantaneously coming to rest. a) Find the spring coefficient (or stiffness) of the second spring. K_2. b) The mass then rebounds off second spring and travels back hitting the first spring. How much does it now displace the first spring before coming instantaneously to rest?

Explanation / Answer

A) work done by all forces = change in KE

fk*d + 0.5k1*x1^2 - 0.5k2x2^2 =0

- 1.2*0.5 +200*0.1^2 = 0.5*0.2^2 k2

k2 = ( - 1.2*0.5 +200*0.1^2) /(0.5*0.2^2)

= 70 N/m

B) 200x^2 = 35*0.2*0.2 - 1.2*0.5 =0.8

x = sqrt (0.004)

= 0.0632 m answer

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