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 = 38.0 J and a maximum displacement from equilibrium of 0.214 m.

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

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

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

(d) What is the speed of the block when its displacement is 0.160 m?
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 = 0.214 m on a rough surface so that it loses 14.3 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

A horizontal block-spring system with the block on a frictionless surface has total mechanical energy E = 37.8 J and a maximum displacement from equilibrium of 0.238 m.
(a) What is the spring constant?
N/m

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

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

(d) What is the speed of the block when its displacement is 0.160 m?
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 = 0.238 m on a rough surface so that it loses 14.8 J by the time it reaches its first turning point (after passing equilibrium at x = 0). What is its position at that instant?
m

a) Total energy = 1/2 . k . x^2

37.8 = 0.5 . k . 0.238^2

k = 75.6 / 0.0566 = 1335 N/m

b) 37.8 J

c) 37.8 = 0.5 . m . 3.45^2

m = 6.35 kg

d) V = V(max) . cos

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