2.A frictionless spring of spring constant 500 N/m has one end attached to a ver

Question

2.A frictionless spring of spring constant 500 N/m has one end attached to a vertical wall and the other end to a block of mass 3.0 kg, which is free to move in one dimension on a horizontal frictionless table. When the spring is relaxed, the block is at x = 0. Now the block is pulled to a displacement of 20 cm and left to oscillate. Assume no friction.

e. At what positions in the oscillation does the maximum Elastic Potential Energy occur?
f. What is the maximum kinetic energy (KE)?
g. What is the maximum speed of the block?
h. What is the speed of the block when it is at x = - 10 cm?

Explanation / Answer

e) at extreme positions i.e. x = 20cm and -20 cm.



f) KEmax = 0.5*k*0.2*0.2 (by energy conservation

KEmax = 10 J



g) KEmax = 10 = 0.5*m*v*v (for max speed, KE is also maximum)

v = 2.582 m/s



h) by energy conservation,

0.5*m*v*v = 0.5*k*0.1*0.1

v = 1.291 m/s

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