A horizontal block-spring system with the block on a frictionless surface has to

Question

A horizontal block-spring system with the block on a frictionless surface has total mechanical energy E = 47.7 J and a maximum displacement from equilibrium of 0.274 m.

(a) What is the spring constant?
1270.7 N/m

(b) What is the kinetic energy of the system at the equilibrium point?
  47.7 J

(c) If the maximum speed of the block is 3.45 m/s, what is its mass?
8.02 kg

(d) What is the speed of the block when its displacement is 0.160 m?
2.8 m/s

(e) Find the kinetic energy of the block at x = 0.160 m.
______ J

(f) Find the potential energy stored in the spring when x = 0.160 m.
______ J

(g) Suppose the same system is released from rest at x = 0.274 m on a rough surface so that it loses 13.9 J by the time it reaches its first turning point (after passing equilibrium at x = 0). What is its position at that instant?
______ m

Explanation / Answer

allowed to answer only 4 sub parts so I am answering first 4 parts

e ) KE = 0.5 * 8.02 * 2.8^2 = 31.4384 J ============answer)

f) PE = 47.7 – 31.4384 = 16.2616 J ============answer)

g ) 33.8 J = 1/2 * 1270.7 . x^2

x = 0.2307 m

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