In science, work is done only when a force moves an object in the direction of the force, and its size is the force times the distance moved: W = Fd.
So however hard you push on a wall, if the wall does not budge, the work done is zero.
Doing work on an object transfers that much energy to it, increasing its kinetic energy or its potential energy.
In the picture below, change the force and the distance, and the distance the box is pushed, the work done and the energy passed to the box all change together.
Work in science
📦 Everyday work and scientific work
①In everyday speech, studying or standing for a long time can be called work
②In science, work is done only when a force acts on an object and the object moves in the direction of the force
③Push hard on a wall that does not move and the distance is zero, so the work is zero too
④Carrying a bag while walking on level ground, the lifting force (upward) is at right angles to the motion (sideways), so the lifting force does no work
seegongsik.com
The work W = Fd done in pushing a box a distance d with a force F, and the energy passed to the box
50 N
5 m
Work and energy
⚡ Energy is the ability to do work
①Doing work on an object increases its energy by the amount of work done
②Lifting an object increases its potential energy
③Pushing an object to make it faster increases its kinetic energy
④The other way round, an object that has energy can do work on something else; water falling from a height turning a waterwheel is an example
Kinetic energy and potential energy
🔋 Energy in motion and in height
①Kinetic energy is the energy of a moving object; it is proportional to the mass and to the square of the speed
②Potential energy is the energy of an object raised up; it is proportional to the mass and to the height
③Kinetic energy plus potential energy is called mechanical energy
④Without friction or air resistance, mechanical energy is conserved
Summary
Definition of work
W = F × d
work (J) = force (N) × distance moved in the direction of the force (m)
Kinetic energy
Ek = 12mv2
Proportional to the mass and to the square of the speed
Potential energy
Ep = mgh
mass × gravitational acceleration (about 9.8 m/s²) × height
🎯 Points that often come up
①work = force × distance moved in the direction of the force, measured in J (= N·m)
②If the force is at right angles to the motion, or the distance is zero, no work is done
③Doing work on an object transfers that much energy to it
④Without friction, kinetic energy plus potential energy stays constant
⑤1 J is the work done by a force of 1 N moving an object 1 m in its direction
Worked examples and unit test
Example 1
A force of 10 N moves an object 5 m in the direction of the force. How much work is done, in J?
1
The force and the motion are in the same direction, so work = force × distance.
2
work = 10 N × 5 m = 50 J.
▸ 50 J
The same 50 J could be done by pushing with 25 N for 2 m. Work is force times distance, so neither one alone decides it.
Example 2
An object of mass 2 kg is moving at 3 m/s. What is its kinetic energy in J? (kinetic energy = ½mv²)
1
kinetic energy = ½ × mass × speed².
2
½ × 2 kg × (3 m/s)² = ½ × 2 × 9 = 9 J.
▸ 9 J
Kinetic energy depends on the square of the speed, so the same object at 6 m/s has four times as much: 36 J.
Unit Test
Which statement about work and energy is correct?
①No matter how hard you push a wall, if it does not move the work done is zero
②The unit of work is the newton (N)
③Kinetic energy is directly proportional to speed
④Potential energy is the same regardless of height
⑤Work is done even when the force is perpendicular to the motion
▸ ① No matter how hard you push a wall, if it does not move the work done is zero
1
The unit of work is the joule (J) (② wrong), and kinetic energy is proportional to the square of speed (③ wrong).
2
Potential energy mgh is proportional to height (④ wrong), and when the force is perpendicular to the motion the work is zero (⑤ wrong); with no movement the work done is zero (① correct).