Understanding Kinetic Energy and Work in Physics

1. Physics Dr. J Seale

2. Kinetic Energy • The kinetic energy (K) is the energy associated with the state motion of an object. • An object of mass m and speed v, where v is well below the speed of light, is defined as • K = ½ m v2

3. Work : • Work (W) is the energy transferred to or from an object by means of a force acting on the object. Energy transferred to an object is positive work, and energy transferred from an object is negative work. • W = F · x

4. Work done by gravitational force Because the change in height is and displacement are in a line (cos0 = 1) • W = mgh

5. Hooke’s Law • F = -kd • Ws = ½ kx2i -1/2kx2f

6. Work by Variable Force: • Consider work done by a variable force over a very short distance: • W = F(x)·Δx • As Δx approaches zero: W = ∫ F(x) dx • In three dimensions: • W = ∫F(x)dxi + ∫F(y)dyj + ∫F(z)dzk

7. Power: • the rate at which work is done. • P = W/ Δt • P = F · v

8. Kinetic Energy: • K = ½ m v2

9. Work done by gravitational force • : W = mgh • Gravitational potential energy: Ug = mgh

10. Work done by elastic element • : Ws = ½ kx2i – ½ kx2f • Elastic potential energy: Us = ½ k x2

11. Work and Energy • Work • ΔU = -W = F Δx • F = dU/dx

12. Work and Energy • Work is energy transferred to or from a system by means of an external force acting on that system. • W =ΔK + ΔU

13. Conservation of Energy • The total energy of a system can change only by amounts of energy that are transferred to or from the system. • W =ΔK + ΔU + ΔEth + ΔEint • The total energy E of an Isolated system cannot change • ΔK + ΔU + ΔEth + ΔEint = 0

14. Closure • Kinetic Energy: K = ½ m v2 • Work : W = F · x • Gravitational Potential Energy: • W = mgh • F = -kd • Ws = ½ kx2i – ½kx2f • Power: P = F · v