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Dynamics

3. Dynamics

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3. Dynamics — CAMBRIDGE AS & A LEVEL PHYSICS 9702 — COMPLETE NOTES notes: Apply Newton's laws, momentum, drag and terminal velocity, and the conservation of momentum in elastic and inelastic collisions to solve problems.Mass — the amount of matter in an object and the property th…

  • Balanced forces
  • Time of impact
  • Drag force
  • Car on a straight road
  • Reducing drag
  • Negligible air resistance

Part 1 of 13Mass and weight

1Mass
— the amount of matter in an object and the property that resists changes in motion; a scalar in kilograms (convert grams by dividing by 1000).
2Weight3 points
— the force on a mass due to a gravitational field: W = mg, a vector in newtons.
  • On Earth g = 9.81 m s−2 (equivalently 9.81 N kg−1).
  • On the Moon g = 1.63 N kg−1, so an object weighs about one-sixth as much.
  • Mass does not change with location; weight does.
3Free fall1 point
— motion under gravity alone; without air resistance, all bodies near the Earth fall with the same acceleration regardless of mass.
  • A larger planet or object has a greater gravitational field strength.

Part 2 of 13Newton's first law

  • Statement — a body stays at rest or moves with constant velocity unless acted on by a resultant force.
  • Balanced forces — the object is in equilibrium: resultant force zero and no change in motion.
    • A book at rest on a table has weight balanced by the table's normal contact force.
  • Unbalanced forces — a resultant force makes the object speed up, slow down or change direction (a change in velocity).

Part 3 of 13Newton's second law

  • Statement — a resultant force causes a change in motion in the direction of the force; the rate of change of momentum is proportional to the force.
  • Equation — F = ma, where F is the resultant force in newtons, m the mass in kg and a the acceleration in m s−2.
    • The resultant force is the vector sum of all forces; choose a positive direction and keep it.
    • Acceleration always has the same direction as the resultant force.
    • If the resultant force is along the motion the object speeds up; against it, the object slows down.

Part 4 of 13Newton's third law

  • Statement — when two bodies interact, the forces they exert on each other are equal in size and opposite in direction.
    • A third-law pair must be the same type of force, equal in size, opposite in direction, and acting on different objects.
    • Weight and the normal contact force on a book are not a pair: they act on the same object and are different types, so that example illustrates the first law.
    • The Earth pulling the book down pairs with the book pulling the Earth up.
    • Avoid the phrase "every action has an equal and opposite reaction" because it does not say which object each force acts on.

Part 5 of 13Linear momentum

  • Momentum — the product of mass and velocity: p = mv, in kg m s−1.
  • Vector — momentum has direction; with right as positive, an object moving left has negative momentum.
    • Convert to SI units first: grams to kg, km s−1 to m s−1.

Part 6 of 13Force as rate of change of momentum

  • Equation — F = Δp/Δt, with Δp = pfinal − pinitial; force and momentum are vectors.
    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)
    • A negative force acts opposite to the chosen positive direction, and the body exerting it feels an equal and opposite force (third law).
  • Time of impact — for the same Δp, a longer contact time gives a smaller force, and a shorter time gives a larger force.

Part 7 of 13Drag and air resistance

  • Drag force — a force opposing the motion of an object through a fluid (gas or liquid); it increases with speed and depends on shape.
  • Car on a straight road — compare the driving force with the resistive forces.
    • Accelerating: driving force greater than the resistive forces.
    • Constant velocity: driving force equal to resistive forces.
    • Decelerating: driving force less than resistive forces.
  • Reducing drag — streamlining, such as a cyclist's posture and helmet.
  • Negligible air resistance — assume there is no drag.

Part 8 of 13Terminal velocity

  • The object is released; the only significant force is weight, so it accelerates at g.
  • As the speed increases the drag grows, so the resultant force (weight − drag) and the acceleration decrease.
  • When drag equals weight the resultant force is zero and the acceleration is zero.
  • The object then falls at constant speed, the terminal velocity, the maximum speed it can reach.
  • The velocity–time graph curves with a gradient that falls to zero.
  • A heavier object has a greater weight and so a greater terminal velocity.
  • When a parachute opens the skydiver decelerates to a lower terminal velocity; they do not move upwards.

Part 9 of 13Conservation of momentum

  • Principlethe total momentum before a collision equals the total momentum after, provided no resultant external force acts.
  • Vector sumsopposite momenta cancel; a rebounding object has negative velocity after the collision; a stationary object has zero momentum.
  • Internal and external forcesinternal forces act between parts of the system (such as a spring or tension); external forces (weight, friction) act from outside.
  • Closed systema system with no external forces acting on it is closed or isolated.
  • Equation for two objectsmAuA + mBuB = mAvA + mBvB, with signs showing direction.

Part 10 of 13Collisions in two dimensions

  • Momentum is a vector, so resolve it into perpendicular components and conserve each separately.
  • Be sure which component uses cosine and which sine.

Part 11 of 13Elastic collisions

  • Elastic collision — a collision in which kinetic energy is conserved (Ek = ½mv2, a scalar that is never negative).
    What the symbols mean: Ek = kinetic energy (J) · m = mass (kg) · v = speed (m s−1)
  • Relative speed — in a perfectly elastic collision, the relative speed of approach equals the relative speed of separation.

Part 12 of 13Inelastic collisions

  • Inelastic collisionmomentum is conserved but kinetic energy is not; some is transferred to other stores (heat, sound, deformation).
  • Perfectly inelasticthe objects stick together and move as one body of combined mass.
  • Testcompare the kinetic energy before and after: if it decreases, the collision is inelastic.

Part 13 of 13More from the specification

  • LinearA graph that is a straight line through the origin, so resistance is constant.
  • Linear momentumThe product of mass and velocity.
  • Common velocityVelocity shared by objects that stick.

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