Physics OCR Chapter 4 (Forces in Action)

Force, Mass, and Acceleration

F = m a 

Mass and Weight

• Mass and weight are two very different quantities
  • Mass in kg is constant for a specific object or particle
  • Weight in N or (kg m s⁻²) has a variable magnitude depending upon location

W = m g 

Centre of Mass and Centre of Gravity

Is the point in which force acts through

Finding Centre of Gravity

• A freely suspended object will come to rest with its centre of gravity below the point of suspension
• Then use a plumb-line, draw a line along the object where the plumb line rests
• Then repeat, the point at which the two lines cross is the centre of gravity

Representing Forces

• Each force vector is shown by a labelled arrow 
• Each arrow is drawn to the same scale ∴ the longer the arrow the greater the force

Moving Through a Fluid

• Objects moving through fluids (e.g. air, water) experience a drag force from the fluid 
• The magnitude of the drag force depends on several factors:
  • Shape of object (cross-sectional area)
  • Speed of object
  • Texture of object
  • Density of fluid
• Drag force ∝ Speed ²
  • When speed doubles, drag force increases by a factor of four

Terminal Velocity

• The instant an object begins to fall there is no drag force and the net force = mg 
• As the object falls its speed increases ∴ drag force increases, thus reducing the net force
• The instantaneous acceleration of the object then becomes less than "g"
• Terminal Velocity is reached when drag force is equal to weight

The Moment of a Force

• The moment of a force is the turning effect of a force about some axis or point

Moment = Force x Perpendicular distance of the line of action of force from the point of rotation

Moment = Fx

The principle of Moment: For a body in rotational equilibrium:
          ∑ of anticlockwise moments = ∑ of clockwise moments

Couples: A pair of forces that are parallel but along different lines that oppose one another 

Torques of a Couple

Moment = (F x d/2) + (F x d/2) = Fd

The moment of a couple is known as a torque

Torque of a couple = one force x perpendicular separation between forces = Fd

Forces in Equilibrium

To add three vector forces you extend the procedure for adding two vectors:

Three coplanar forces acting on an extended object can also be applied using free body diagrams

Density - of a substance is defined by Mass per Unit Volume

Density (p) = Mass (m) / Volume (V)

Calculating Density 

• The mass and volume need to be known:
  • Mass can be measured using a balance
  • Volume can be measured using a ruler or through displacement

Pressure - is the normal force exerted per unit cross-sectional area

Pressure (p) = Force (F) / Area (A)

Pressure in Fluids

• Fluids , such as air, exert pressure on surfaces because of constant bombardment by their molecules

Liquids

p = hpg 

p = pressure    h = hight of column    p = desity of the liquid    g = acceleration of free fall

     ** IF CALCULATING IN SEA WATER DON'T FORGET THE ATMOSPHERE ABOVE **

Upthrust

• Calculate force at the top surface, and the bottom surface, then find the difference

Upthrust = Axpg 

A = Area   x=Difference in height   p = Density of fluid   g = Acceleration of free fall