Unit 7: Work and Kinetic Energy
Work as a force integrated along a path, and the work-energy theorem that turns force problems into energy bookkeeping.
5 topics · 16 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Work Done by a Constant Force
- How it worksHow does only the force component along the direction of motion end up doing any work at all?
- Worked exampleFind the work done dragging a 15 kg crate 6 m with a 40 N force applied at 30 degrees above horizontal.
- Common mistakeWhy doesn't holding a heavy object perfectly still count as doing work on it?
Your turn1 of 2
A crate is dragged 9 m across a floor by a force of 59 N applied at 56 degrees above horizontal. How much work is done on the crate, in joules?Work Done by a Variable Force
- How it worksHow does integrating force over distance capture the work done even when the force keeps changing?
- Worked exampleFind the work done stretching a spring with k = 200 N/m from 0 to 0.1 m.
- Going furtherWhat happens to the work integral when force and displacement point in opposite directions the whole time?
Your turn1 of 2
A spring with spring constant 309 N/m is stretched from 0 to 0.212 m. How much work is done stretching it, in joules?Kinetic Energy
- How it worksHow does the v-squared in kinetic energy come directly out of integrating F = ma over distance?
- Worked exampleFind the kinetic energy of a 1500 kg car moving at 28 m/s.
- Common mistakeWhy isn't kinetic energy a vector the way velocity and momentum are?
Your turn1 of 2
A 1636 kg car moves at 26 m/s. What is its kinetic energy, in joules?The Work-Energy Theorem
- How it worksHow does the work-energy theorem fall directly out of Newton's second law and a bit of calculus?
- Worked exampleFind the final speed of a 4 kg block starting from rest after 80 J of net work is done on it.
- Worked exampleFind the net work needed to slow a 1000 kg car from 20 m/s down to 10 m/s.
- Common mistakeWhy doesn't negative work on an object always mean it's losing all of its energy?
Your turn1 of 2
A 7 kg block starts from rest, and 137 J of net work is done on it. What is its final speed, in meters per second?Power
- How it worksHow does power measure the rate at which work gets done, not just the total amount done?
- Worked exampleFind the power output of an engine that does 50000 J of work in 4 seconds.
- Going furtherWhat happens to the power required to hold a car at constant speed when its speed doubles but drag scales with v2?
Your turn1 of 2
An engine does 72678 J of work in 7 s. What is its power output, in watts?