Use this information to answer the next X questions A 3.5 kg object falls from a

Question

Use this information to answer the next X questions A 3.5 kg object falls from a height of h 0.50 m onto a massless, L0.50 m long, spring. Upon collision, the mass becomes attached to the spring and enters into simple harmonic motion in the vertical z direction (take up to be positive z). In the diagram. ?2 represents the change in the equilibrium position of the spring from when the mass is attached versus the spring alone, and A represents the amplitude of the simple harmonic oscillations Az 5. If the change in equilibrium position is |? = 0.16 m. what s the spring constant? A) 214 N/m B) 1340 N/m C) 101 N/m D) 18.7 Nm E) 429 N/nm 6. The maximum potential energy of the system in oscillation is equal to the total potential energy of the mass prior to oscillation: V-mg(h + |?:). If |??-0.05 m, what is the amplitude of the oscillations of the simple harmonic motion'? A) 0.23 m B) 0.32 m C) 0.19 m D) 0.071 Im E) Insufficient information to answer the problem

Explanation / Answer

5.

Use law of conservation of energy,

PEg=PEs

mgh=1/2k?z2

k=(2mgh)/?z2

Plugging values,

k=(2*3.5*9.8*0.50)/(0.16^2

k= 1340 N/m

6.

Use law of conservation of energy

Emax= PEi

1/2*k*A^2 = mg(h+ ?z)

1/2*1340*A^2 = 3.50*9.8*(0.50+0.05)

A= 0.19m

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