Please show every step of the solution for this one question: A 2.50-kg mass is

Question

Please show every step of the solution for this one question:

A 2.50-kg mass is pushed against a horizontal spring of force constant 25.0 N/cm on a frictionless air table. The spring is attached to the tabletop, and the mass is not attached to the spring in any way. When the spring has been compressed enough to store 11 .5 J of potential energy in it, the mass is suddenly released from rest. (a) Find the greatest speed the mass reaches. When does this occur? (b) What is the greatest acceleration of the mass, and when does it occur?

Explanation / Answer

a)

Greatest Speed

KE=(1/2)mVmax2

11.5=(1/2)*2.5*Vmax2

Vmax=3.03 m/s

b)

KE=(1/2)KX2

11.5=(1/2)*(25*102)*X2

X=0.0959 m

Force

F=KX =25*102*0.0959

F=239.8 N

acceleration

a=F/m =239.8/2.5

a=95.92 m/s2

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