I WILL Lifesaver. Thank you Consider the force-displacement graph for a spring s

Question

I WILL Lifesaver. Thank you

Consider the force-displacement graph for a spring shown. Determine (a) the spring constant, (b) the potential energy stored when the spring is stretched from x = 0 to x = 4.0 cm. (c) the change in the potential energy stored in stretching the spring from x = 1.0 cm to x = 4.0 cm. A cart having a mass M = 180 g on a friction free horizontal surface is accelerated from rest by the launching spring of problem 2. What is the cart's final speed if the spring's potential energy with a compression of 4.0 cm is completely transferred to the cart?

Explanation / Answer

F=kx
a)So spring constant is the slope of force displacement graph
k= 2/.01 = 200N/m
b)potential energy in the spring =.5kx^2
so the energy stored x=0->x=4 = .5k4^2/10000 -.5K0^2 = .5*200*4^2/10000 = 0.16j
C)From x=1 ->x =4
.5k4^2/10000-.5k1^2/10000 = 0.14J

Kinectic energy =.5mv^2 and this energy weil come from  0.16j in spring

we have

.5*120*v^2 /1000 =.16 v= 1.63m/sec

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