1. A spring system consists of a stationary spring and a 100-gram mass attached

Question

1. A spring system consists of a stationary spring and a 100-gram mass attached to one end that slides along a horizontal frictionless surface. When a horizontal force of 10.0 N is applied to the mass, the spring stretches 30.0 cm.

a) How much total energy is in the spring?

b)What is the speed of the mass as it passes through a point 15.0 cm from its equilibrium point?

c)What is its speed at the exact instant when it passes through its equilibrium position?

d)Why aren't these speeds in a ratio of 1:2?

Explanation / Answer

a) E = 0.5kx2

kx = F

k = F/x = 10/0.3 = 33.33 N/m

E = 1.5 J

b) 1.5 = 0.5mv2 + 0.5kx'2

1.5 = 0.5 x 0.1 x v2 + 0.5 x 33.33 x 0.152

v = 4.74 m/s

c) 1.5 = 0.5mv2

v = 5.477 m/s

d) becoz the function of velocity is not linear. its an cosine or sine function. thts why speed is not in ratip 1:2

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