Mass and Weight

Mass:

  • Measure of quantity of matter in an object at rest.
  • Independent of location.

Weight:

  • Gravitational force acting on an object with mass.
  • Dependent on gravitational field strength.
  • Formula: $$g = \frac{W}{m}$$ (where $g$ is gravitational field strength, $W$ is weight, $m$ is mass).

Comparing Weights and Masses:

  • Use a balance to compare masses directly.
  • Balance compares gravitational forces (weights) acting on two objects.

Density and Buoyancy

Density:

  • Mass of a substance per unit volume.
  • Formula: $$\rho = \frac{m}{v}$$

Determining Density:

  • Liquid: Direct measurement using measuring cylinder.
  • Regular Solid: Measure mass and volume.
  • Irregular Solid: Use displacement method with water.
    • Volume = Volume of liquid displaced. Image description: Object submerged in water displacing liquid in a measuring cylinder

Floating Condition:

  • An object floats if its density is less than or equal to the fluid it is submerged in.
  • One liquid floats on another if it is less dense.

Image comparing liquid densities

Effects of Forces

Forces produce changes in size, shape, or motion.

Load-Extension Graphs:

  • X-axis: Load (Force). Y-axis: Extension.
  • Linear region: Hooke’s Law applies.
  • Limit of Proportionality: Point beyond which the graph becomes non-linear. Image description: Load-extension graph showing linear and non-linear regions

Resultant Force (Along a Line):

  • Forces in same direction: Add.
  • Forces in opposite direction: Subtract.

Newton’s First Law: An object remains at rest or constant speed unless acted on by a resultant force.

Velocity Change: A resultant force changes an object’s velocity (speed or direction).

Friction and Drag:

  • Solid Friction: Force between surfaces impeding motion; produces heating.
  • Drag: Friction in liquids and gases (air resistance).

Turning Effect of Forces (Moment)

Moment: Force multiplied by perpendicular distance from pivot.

  • Formula: $\text{Moment} = \text{Force} \times \text{Perpendicular Distance}$

Principle of Moments:

  • In equilibrium, the resultant moment is zero.
  • Clockwise moments = Counterclockwise moments. Image description: Torque diagram showing forces acting on a lever arm around a pivot

Equilibrium: No resultant force AND no resultant moment.

Solid Friction: Force between surfaces impeding motion.

Circular Motion

Centripetal force

  • Force Direction: Perpendicular to motion.
  • Effect of Force Increase:
    • Speed increases (if mass and radius constant).
    • Radius decreases (if mass and speed constant).
  • Effect of Mass Increase: Requires increased force for same speed and radius.

Centre of Gravity

Center of Gravity Definition: Point where the object would balance under the influence of its own weight.

Finding Centre of Gravity:

  • Experiment with an irregularly shaped plane lamina: Suspend from two different points, mark vertical lines, intersection is CoG. Image description: Suspended lamina with vertical strings meeting at a dot

Lower Centre of Gravity increases stability.

Momentum

Momentum:

  • Mass multiplied by velocity.
  • Formula: $$p = mv$$

Impulse: Force applied over a time interval.

  • Formula: $$\text{Impulse} = F\Delta t = \Delta(mv)$$

Conservation of Momentum: In an isolated system, total momentum remains constant.

Resultant Force:

  • Rate of change of momentum.
  • Formula: $$F = \frac{\Delta p}{\Delta t}$$

Pressure

Pressure:

  • Force per unit area.
  • Formula: $$p = \frac{F}{A}$$

Everyday Examples: Tyre pressure, hydraulic jacks, syringe.

Pressure in Liquids:

  • Increases with depth and density.
  • Formula: $$\Delta p = \rho g \Delta h$$ Image description: U-tube manometer showing pressure difference with depth