please show formulas A horizontal block-spring system with the block on a fricti

Question

please show formulas

A horizontal block-spring system with the block on a frictionless surface has total mechanical energy E 41.8 J and a maximum displacement from equilibrium of 0.288 m. Neglect the mass of the spring a) (20 points) AFTER YOU READ THE ENTIRE PROBLEM DRAW A good physics liagram BEFORE A good physics diagram BEFORE YOU START CALCULATING. b) (20 c) (20 points) What is the kinetic energy of the system at the equilibium point? d) (20 points) If the maximum speed of the block is 3.45 m/s, what is its mass? e) (10 points) Find the kinetic energy of the block at x 0.160 m. f) (10 points) Find the potential energy stored in the spring when x - 0.160 m points) What is the spring constant?

Explanation / Answer

a)

total mechanical energy

Etot=(1/2)KA2

41.8=(1/2)*K*0.2882

K=1007.9 N/m

b)

at equilibrium point

KE=Etot=41.8 J

c)

41.8=(1/2)*m*3.452

m=7.02 kg

d)

E=(1/2)mV2+(1/2)Kx2

41.8 =(1/2)[7.02*V2+1007.9*0.162]

V=2.87 m/s

e)

U=(1/2)Kx2=(1/2)*1007.9*0.162=12.9 J

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