Summary — What This Chapter Covers
- Mass is the property of an object that resists change in its motion.
- Resultant force F = ma; the acceleration is always in the direction of the resultant force.
- Momentum p = mv; force = rate of change of momentum, F = Δp/Δt.
- Weight W = mg is the effect of a gravitational field on a mass.
- Friction and drag oppose motion; drag increases with speed, so a falling object can reach terminal velocity.
- Momentum is conserved in all interactions of an isolated system; kinetic energy is conserved only in elastic collisions.
1. Momentum and Newton's Laws of Motion
Newton's laws
Force, mass and momentum
Newton's first law: an object remains at rest or moves with constant velocity unless acted on by a resultant force. Second law: the resultant force on an object is proportional to its rate of change of momentum (and in the same direction); with suitable units F = Δp/Δt, which for constant mass becomes F = ma. Third law: if body A exerts a force on body B, then B exerts a force on A that is equal in magnitude, opposite in direction and of the same type.
Third-law pairs act on different bodies, so they never cancel each other. The weight of a book and the table's push on it are not a third-law pair (they act on the same body and are different types of force).
Weight is the gravitational force on a mass: W = mg. Mass (kg) is a scalar that measures resistance to change in motion; weight (N) is a force.
Key equations
p = mv F = Δp/Δt F = ma W = mg impulse = FΔt = Δp
Worked Example
A ball of mass 0.15 kg hits a wall at 20 m s−1 and rebounds along the same line at 15 m s−1. Contact lasts 0.010 s. Find the average force on the ball.
Practice Question
A person of mass 60 kg stands on scales in a lift that accelerates upwards at 1.5 m s−2. What do the scales read?
2. Non-uniform Motion
Non-uniform motion
Friction, drag and terminal velocity
Friction acts between surfaces in contact and opposes relative motion. Drag (viscous force, including air resistance) acts on an object moving through a fluid; in the simple model drag increases as speed increases.
For an object falling from rest: at first the speed is small, drag is small and the acceleration is about g. As the speed rises, drag rises, the resultant force (W − D) falls and the acceleration decreases. When drag equals weight the resultant force is zero and the object falls at constant terminal velocity. The velocity–time graph starts with gradient g and curves over to a horizontal line.
A skydiver who opens a parachute suddenly has a much larger drag than weight: the resultant force is upwards, the skydiver decelerates, drag falls with speed, and a new, lower terminal velocity is reached.
Falling with drag D
resultant force = mg − D a = (mg − D)/m terminal velocity when D = mg
Worked Example
A skydiver of mass 80 kg falls with air resistance 300 N at one instant. Find her acceleration then, and the air resistance at terminal velocity.