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?moves an object a distance,?d?metres?in the same direction as the?line of action?of the force the?work done,?W??, by the force is

• • 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 (N m), 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
  • 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 move the object forwards against 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?N2L?to find one of the components in the formula
• 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 necessary, resolve the forces acting in the direction of motion to find the magnitude of the force acting on the object

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

How do we use work done on an inclined plane?

• The object will be said to travel up the?line of greatest slope?on an?inclined plane
• If the?coefficient of friction?is involved then the weight will need to be resolved to find the value of the?normal reaction force,?R
  • There is no work done by the normal reaction force as it acts perpendicular to the direction of motion
• The?work done against gravity?can be found by using right – angled trigonometry to find the change in vertical height of the object