Work-Energy Principle
What is the Work-Energy Principle?
- The Work-Energy Principle has many forms, but is in essence an energy balance
- the final amount is the initial amount plus any energy put in (or minus any taken out)
- it's a bit like money in a bank account!
- The principle can be written as:
- total final energy = total initial energy ± work done by non-gravitational forces
- or, using subscripts for final and initial,
- "total energy" here means the sum of Gravitational Potential Energy and Kinetic Energy
- e.g.
- Non-gravitational forces are any external forces that are not related to gravity
- e.g. frictions, tensions, driving forces, etc
- but wouldn't include weight, , because work done against gravity has already been considered in the GPE part
- Use + for work done by forces that "help" the object to move forwards
- e.g. tension in a string pulling forwards, a driving force, etc
- Use - for work done by forces that "hinder" (resist) the object from moving forwards
- e.g. friction, tension in a string pulling backwards, a resistance force, air resistance, etc
- total final energy = total initial energy ± work done by non-gravitational forces
- Some situations may have more than one form of work done
- add or subtract each one, depending whether they help or hinder
How else can the Work-Energy Principle be written?
- You can write the Work-Energy Principle in terms of gains or losses in KE and GPE
- but this method can cause a lot of sign errors!
- Write out each term in the original version, "total final energy = total initial energy ± work done by non-gravitational forces"
- use subscripts for final and initial
- group together KEs and GPEs as an overall change ("final - initial")
- change in KE = - change in GPE ± WD
- you can read this as gain in KE = loss in GPE ± WD
- but some situations lose KE, so the gain is negative (you need to be really careful with the signs and what "loss" means!)
- use subscripts for final and initial
- The first method (energy balance) works for every situation, but this "gain-loss" method needs adapting for each situation
Can I use the Work-Energy Principle on an inclined plane?
- Yes, and remember to calculate work done as "the component of force in the direction of motion" × "distance moved in direction of motion"
- in this case, the direction of motion is parallel to the slope
- You may also need to calculate the final vertical height for GPE
- e.g. using trigonometry, with the distance in the direction of the slope as the hypotenuse
Exam Tip
- If a question asks you to find something "using the work-energy principle", don't use Newton's 2nd Law with SUVAT!
Worked example
A dog uses a constant force of N to push its toy of mass 0.5 kg up a rough slope inclined at 20° to the horizontal. The force, , acts parallel to the slope. The toy starts from rest and, after moving 10 metres up the line of greatest slope, it is travelling at 1 ms-1. The coefficient of friction between the toy and the slope is 0.1.
Use the work-energy principle to find .