Topic 7: Work and Energy

work is energy transmitted to a particle by a force as it is moved from one place to another

what is work

• W = ∑FΔs

  • ∑F - net force magnitude

  • Δs - distance travelled in the same direction as the net force

what is the equation for the total work done

when the force vector is opposite the displacement vector

when is work done negative

energy is added to the particle

what does positive work done mean

energy is removed from the particle

what does negative work done mean

the rate at which a force does work

what is power

P = Fv

what is the equation for instantaneous power

• P_average = U/Δt

  • U - work done

what is the equation for average power

the work done to take a particle from rest to a velocity, v

what is kinetic energy

T = ½ mv²

what is the equation for kinetic energy

the work done by a conservative force is independent from the path taken - it only depends on the start and end positions

what is the concept of potential energy

the work done against gravity to raise a particle a distance h above an arbitrary reference plane

what is gravitational potential energy

V_G = mgh

what is the equation for gravitational potential energy

U_1→2 = -ΔV_G

how does gravitational potential energy relate to work done

work stored in a deformed spring

what is elastic potential energy

• F = kx

  • where k is the spring stiffness (constant)

  • x is the spring extension (or compression)

    • x = current spring length - unstretched spring length

  • the spring force always opposes the extension

what is the equation for Hooke’s law

V_e = 1/2kx²

what is the equation to calculate elastic potential energy

U_1→2 = -ΔV_e

how does elastic potential energy related to work done

U_1→2 = ΔT (total work done = change in kinetic energy)

what is the simple work-energy equation

U’_1→2 = ΔT + ΔV_G + ΔV_E

what is the modified work-energy equation

when U’_1→2 = 0

when do we have conservation of energy

1. identify provided information and what is required

2. draw a FBD or FBDs

   • choose a representative location or locations

3. choose a coordinate system

   • define a reference height

4. state any kinematic constraints

5. write equations of motion

   • U’_1→2 = ΔT + ΔV_G + ΔV_E

6. solve equations for required information

7. check that your answer makes sense

what are the steps involved in solving kinetics of particles problems using work-energy methods