Consider a non-ideal spring. The spring exerts a force -15.0 N/m x + 3.00 N/m^2

Question

Consider a non-ideal spring. The spring exerts a force -15.0 N/m x + 3.00 N/m^2 x^2, when it is displaced a distance x from its equilibrium Length. The displacement x is positive if the spring is stretched and negative if the spring is compressed. (a) What force does the spring exert when stretched 5.00 cm? (b) How much work Is required to stretch the spring 5.00 cm from equilibrium? (C) How much work Is required to compress the spring from equilibrium by 5.00cm? (d) The spring is used in a spring gun to project a 10.0 g ping-pong ball. In the gun, the spring is compressed by 5.00 cm before the gun is fired. How fast is the bait traveling after the gun Is fired?

Explanation / Answer

a) x = + 5 cm = + 0.05 m

F = -15 x + 3x^2

F = -(15*0.05) + 3*(0.05^2) N

F = -0.7425 N

so it exert 0.7425 N force in reverse direction

b)
Work done by spring = -15*((x^2)/2) + x^3 = -7.5*(0.05^2) + (.05^3) = -0.018625 J

work required = 0.018625 J

c) same amount = 0.037125 J

d) 0.037125 = (1/2)*0.01*v^2

v^2 = 2*3.7125 = 7.425

v= 2.72m/s

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