work-done

Work done

What does the term work mean in mechanics?

• In Mechanics the word work refers to the work done by a force when it causes an object to move

  • Mechanical work happens when both a force is applied and the object moves

  • A force that is holding an object stationary is not producing any mechanical work

  • The object gains energy due to the work done by forces acting in the direction of motion

  • The object loses energy due to the work done against resistive forces

• The line of action of a force refers to the point of application of the force and the direction the force was applied in

• Work is a scalar quantity, it has size without direction

How do we calculate work done by a force?

• If the point of application of a force of magnitude F N, which moves an object a distance, d metres, is in the same direction as the line of action of the force, then the work done, W , by the force is

(sometimes  is used in place of )

• If the line of action of the force is at an angle to the direction of motion, then the component of the force in the direction travelled is multiplied by the distance instead

  • If the object moves vertically upwards then the work is done against gravity and this calculation becomes

• The units for the work done by a force are Newton metres (Nm), but it is more common to use Joules

  • 1 Joule = 1 N m

  • 1 Joule is equal to the amount of work done by a force of 1 Newton moving an object 1 metre along the line of action of the force

  • 1 Kilojoule is equal to 1000 Joules (1 kJ = 1000 J)

• If the line of action of the force is different to the direction of motion, start by resolving the force into components parallel and perpendicular to the direction of motion

  • When a force of F N is acting at an angle of θ°  to the direction of motion, the component of F acting in the direction of motion will be  and the work done by the force will be 

  • The perpendicular component of the force will produce no work

• The net work done on an object will be equal to the work done by the force that moves the object forwards, in addition to any work done against resistive forces

How do we use work done with N2L (F = ma)?

• If the work done by a force is known it can often be used along with Newton’s second law (N2L) to find one of the components in the formula F=ma

• Often the object will be moving at constant speed so the acceleration of the object will be zero, so the forces acting on the object in the direction of motion will be in equilibrium

STEP 1: Draw a diagram or add all the forces to the diagram given in the question

STEP 2: If the line of action of the force is at an angle to the direction of motion, find the component of the force parallel to the direction of motion

STEP 3: If there is more than one force, resolve the forces to find the resultant component acting in the direction of motion

STEP 4: Use W = Fs to find the work done by the force on the object

• If the problem involves friction, you may have to resolve perpendicular to the plane to find the value of the normal reaction force, R, and then use 

  • If the force overcomes friction to cause an object to move, it is said to do work done against friction

  • The object will be moving, so friction will be limiting and <img alt=”begin mathsize 14px style bold italic F subscript bold M bold A bold X end subscript bold space bold equals bold italic mu bold italic R end style” data-mathml='<math ><semantics><mstyle mathsize=”14px”><msub><mi mathvariant=”bold-italic”>F</mi><mrow><mi mathvariant=”bold”>M</mi><mi mathvariant=”bold”>A</mi><mi mathvariant=”bold”>X</mi></mrow></msub><mo mathvariant=”bold”> </mo><mo mathvariant=”bold”>=</mo><mi mathvariant=”bold-italic”>μ</mi><mi mathvariant=”bold-italic”>R</mi></mstyle><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″}</annotation></semantics></math>’ height=”23″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2223%22%20width%3D%2276%22%20wrs%3Abaseline%3D%2214%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmstyle%20mathsize%3D%2214px%22%3E%3Cmsub%3E%3Cmi%20mathvariant%3D%22bold-italic%22%3EF%3C%2Fmi%3E%3Cmrow%3E%3Cmi%20mathvariant%3D%22bold%22%3EM%3C%2Fmi%3E%3Cmi%20mathvariant%3D%22bold%22%3EA%3C%2Fmi%3E%3Cmi%20mathvariant%3D%22bold%22%3EX%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%20mathvariant%3D%22bold%22%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%20mathvariant%3D%22bold%22%3E%3D%3C%2Fmo%3E%3Cmi%20mathvariant%3D%22bold-italic%22%3E%26%23x3BC%3B%3C%2Fmi%3E%3Cmi%20mathvariant%3D%22bold-italic%22%3ER%3C%2Fmi%3E%3C%2Fmstyle%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math17f39f8317fbdb1988ef4c628eb’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADRjdnQgDVUNBwAAAVAAAAA6Z2x5ZoPi2VsAAAGMAAAAsmhlYWQQC2qxAAACQAAAADZoaGVhCGsXSAAAAngAAAAkaG10eE2rRkcAAAKcAAAACGxvY2EAHTwYAAACpAAAAAxtYXhwBT0FPgAAArAAAAAgbmFtZaBxlY4AAALQAAABn3Bvc3QB9wD6AAAEcAAAACBwcmVwa1uragAABJAAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACAAAAAEAAQAAQAAAD3%2F%2Fw