Force, Laws of Motion and Gravitation

Force

A force is a push or a pull. It can change an object's speed, direction, shape or state of rest. Unit: newton (N); 1 N = 1 kg m/s^2.

Contact forces need touching (muscular, friction); non-contact forces act at a distance (gravity, magnetic, electrostatic).

Friction

Friction opposes motion between two surfaces in contact. It depends on the roughness of surfaces and the force pressing them together, not on the contact area (for solids).

• Advantages: we can walk, grip, write, brakes work, nails hold.
• Disadvantages: wear and tear, heat, wasted energy.
• Reduced by: lubricants (oil, grease), polishing, ball bearings, streamlined shapes, wheels.
• Increased by: rough surfaces, treads on tyres, spikes on shoes.
• Fluid friction (drag) acts on objects moving through liquids and gases.

Newton's laws of motion

• Inertia is the tendency of a body to resist a change in its state. Mass is the measure of inertia. A heavier body has more inertia.
• Momentum p = mv (unit kg m/s); it is a vector.
• Impulse = force x time = change in momentum.
• Conservation of momentum: in a collision with no external force, total momentum before = total momentum after.
• Balanced forces do not change motion; unbalanced forces do.

Gravitation

• Universal law (Newton): every object attracts every other with a force directly proportional to the product of masses and inversely proportional to the square of the distance.

F = G m1 m2 / r^2 with G = 6.67 x 10^-11 N m^2 / kg^2

• G is the universal gravitational constant (found by Cavendish). g is the acceleration due to gravity.
• Free-fall acceleration: g = GM / R^2; on Earth g = 9.8 m/s^2.
• Weight W = mg. Mass is constant everywhere; weight changes with g.
• g varies: highest at the poles, lowest at the equator; decreases with height and depth; zero at the centre of the Earth.
• On the Moon, g is about 1/6 of Earth's, so weight is one-sixth. The mass remains the same.
• In free fall (a satellite), objects feel weightless.
• Escape velocity of Earth: about 11.2 km/s. Orbital velocity near Earth: about 7.9 km/s.
• Kepler's laws describe planetary motion: planets move in ellipses with the Sun at one focus; a planet sweeps equal areas in equal times; the square of the orbital period is proportional to the cube of the average distance.

Pressure, density and buoyancy

• Pressure is more when the area is small (sharp knife, nails, pointed needle); less when area is large (wide tyres, camel feet, snow shoes).
• Liquid pressure increases with depth and acts in all directions. Dams are thicker at the bottom.
• Atmospheric pressure at sea level is about 101,325 Pa = 1 atm. A barometer measures it (invented by Torricelli); a manometer measures gas pressure.
• Pascal's law: pressure applied to an enclosed fluid is transmitted equally. Used in hydraulic lift and brakes.
• Buoyancy (upthrust): the upward force on an object in a fluid.
• Archimedes' principle: the upthrust equals the weight of fluid displaced.
• Floating: an object floats if its density is less than the liquid's; it sinks if more. Ships float because the displaced water weighs as much as the ship. Plimsoll line marks safe loading.
• Density of water = 1000 kg/m^3 (1 g/cm^3) at 4 degrees C. Hydrometer measures the density of liquids; lactometer checks milk purity.
• Pressure units: 1 atm = 760 mm of mercury.