Question 3 only Kinetic & Potential energy Write a brief statement of the Work-E

Question

Question 3 only Kinetic & Potential energy Write a brief statement of the Work-Energy Theorem or Kinetic Energy Theorem. (This is not the definition of work.) Consider the force-displacement graph for a spring shown. Determine the spring constant, the potential energy stored when the spring is stretched from x = 0 to x = 4.0 cm, 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

From question (2)

Slope k =F/x = (2/1) = 2 N/cm = 200 N/m

M = 180 g, x = 4cm

From conservation of energy

K1+U1 =K2+U2

0 + (1/2)kx^2 =(1/2)mv^2 +0

(200*0.04*0.04) = (0.18*v^2)

v =1.33 m/s

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