Lesson summary
2.1 Dynamics — AS PHYSICS 9702 notes: Summarise mass and weight, Newton's laws, momentum, drag and terminal velocity, conservation of momentum and collisions.Mass = the property of a body that resists changes in its motion (inertia); it is a scalar in kg and is the same everywher…
- Linear momentum p = mv
- What the symbols mean
- For constant mass
- A longer collision time reduces the average force
- They act on different bodies
- Weight and the normal contact force on a book are not a pair
Section 1 of 9Mass, weight and Newton's first law
1Mass
Mass the property of a body that resists changes in its motion (inertia); it is a scalar in kg and is the same everywhere.
2Weight
Weight the gravitational force on a mass, W = mg, in N; g = 9.81 N kg-1 at the Earth's surface.
3
An astronaut on the Moon has the same mass but less weight.
4First law
- First law a body stays at rest or at constant velocity unless a resultant force acts;
- zero resultant force means equilibrium.
Section 2 of 9Newton's second law and momentum
Newton's second law and momentum
Linear momentum p = mv
- Linear momentum p = mv unit kg m s-1, a vector in the direction of the velocity.
Force
Force the rate of change of momentum: F = Δp ÷ Δt, in newtons.
What the symbols mean: F = force (N) · Δt = time the force acts (s) · Δp = change in momentum (kg m s−1); FΔt is the impulse (N s)
For constant mass
- F = mΔv ÷ Δt = ma, and the acceleration is in the direction of the resultant force.
Impulse
FΔt = Δp, in N s, equal to the area under a force-time graph.
A longer collision time reduces the average force
- A longer collision time reduces the average force crumple zones, airbags and bending the knees.
Section 3 of 9Newton's third law
Newton's third law
Third-law pairs are equal in size, opposite in direction and the same type of force.
They act on different bodies
- They act on different bodies so they never cancel for a single body.
Weight and the normal contact force on a book are not a pair
- Weight and the normal contact force on a book are not a pair they act on the same object and are different types.
Section 4 of 9Drag and terminal velocity
1A body falling through air at first has only weight acting
- A body falling through air at first has only weight acting so a = g.
2As speed increases drag increases
- As speed increases drag increases the resultant force (W − D) and the acceleration decrease.
3When drag equals weight
- When drag equals weight the acceleration is zero and the body falls at terminal velocity.
4On a v-t graph
- On a v-t graph the gradient starts at g and decreases to zero as the curve levels off.
5Opening a parachute
- Opening a parachute drag exceeds weight, so the skydiver decelerates to a new, lower terminal velocity.
Section 5 of 9Conservation of momentum
Conservation of momentum
For an isolated system the total momentum is constant
- For an isolated system the total momentum is constant m1u1 + m2u2 = m1v1 + m2v2.
It follows from the second and third laws
- It follows from the second and third laws the forces on each body are equal, opposite and act for the same time.
In an explosion from rest
- In an explosion from rest total momentum stays zero, so fragments move in opposite directions with m1v1 = m2v2.
In two dimensions
- In two dimensions resolve into components and conserve momentum separately in each of two perpendicular directions.
Section 6 of 9Elastic and inelastic collisions
Elastic
- Elastic both momentum and kinetic energy are conserved;
- relative speed of approach equals relative speed of separation, u1 − u2 = v2 − v1.
Inelastic
- Inelastic momentum is conserved but kinetic energy is transferred to thermal energy, sound and deformation;
- total energy is still conserved.
Kinetic energy Ek = ½mv2 = p2 ÷ 2m, in joules.
Section 7 of 9Verifying conservation of momentum with trolleys
1
Use a friction-compensated runway, tilted slightly so a trolley moves at constant speed.
2
Fit light-gate cards of known length and measure the masses m1 and m2 on a balance.
3
Push trolley 1 through light gate 1 and calculate u1 = card length ÷ time.
4
Let it collide with stationary trolley 2, fitted with Velcro or a pin and cork to stick, or magnets to bounce.
5
Measure the velocity after the collision through a second gate in the same way.
6
Compare total momentum before and after, and compare kinetic energies to classify the collision.
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Mass | The property of a body that resists changes in its motion. |
| Weight | The gravitational force on a mass, W = mg. |
| Linear momentum | The product of mass and velocity. |
| Impulse | Force multiplied by time, equal to the change in momentum. |
| Terminal velocity | The constant velocity reached when drag equals weight. |
| Elastic collision | A collision in which kinetic energy is conserved. |
| Inelastic collision | A collision in which kinetic energy is not conserved. |
| Isolated system | A system with no resultant external force. |
Section 9 of 9Exam technique
1
Using F = ma when the mass changes — use F = Δp ÷ Δt.
2
Saying action and reaction cancel — they act on different bodies.
3
Thinking kinetic energy is conserved in every collision — only momentum always is.
4
Saying terminal velocity means zero velocity or no forces — the forces balance.