Write a brief statement of the Work-Energy Theorem or Kinetic Energy Theorem. (T

Question

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

work energy theorem states that work done by the all forces on the partical is responsible for the chage of kinetic energy of that particle.

in other word you can say that work done on partical by forces is equal to kinetic energy of that partical.

mathematical statement

The work W done by the net force on a particle equals the change in the particle's kinetic energy

KE: W=KE=12mvf21/2mv2i

In general

systems than the particle system mentioned here, work can change the potential energy of a mechanical device, the heat energy in a thermal system, or the electrical energy in an electrical device.

ans 2

part a

F =Kx

K = F/K or we can say that slpoe of line in graph

K =2/1 =2 N/cm = 200N/m

part b

as by above theorem work done = change in potentaial energy

so work done = area under X=0 and X=4 cm and line going through origin

potential energy =1/2 * 7*4*10-2= 0.14J

part c

potentail energy = area under x=1 to x=4

= 1/2 * 7*4*10-2 - 1/2 * 2*1*10-2

   = 0.13 J

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