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4.1.3Linear Momentum

Impulse Equation — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 9 parts Lesson 4 of 13 1 quiz

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Lesson summary

4.1.3 Impulse Equation — AP PHYSICS 1 notes: Define impulse as the product of force and time and calculate it for constant and varying forces.Impulse = the effect of a force acting over a time interval, J = FavgΔt.Unit — N·s, equivalent to kg·m/s, the unit of momentum.Vector — im…

  • From force and time
  • From momentum change
  • From a graph
  • Average versus peak force
  • Including gravity
  • Long interactions

Part 1 of 7What impulse is

Impulse
Impulse the effect of a force acting over a time interval, J = FavgΔt.
Unit
  • N·s, equivalent to kg·m/s, the unit of momentum.
Vector
  • Vector impulse has the direction of the net force; if the average force is zero there is no impulse.
Net force
  • Net force the equation uses the net force on the object.

Part 2 of 7Ways to find impulse

1From force and time
  • J = FavgΔt.
2From momentum change
  • J = Δp = mvf − mvi, usually easiest in a collision.
3From a graph
  • From a graph the area under the force–time graph.
4Average versus peak force
  • Favg gives the same impulse as the real varying force; the peak force can be several times larger.

Part 3 of 7Net force and short collisions

Including gravity
  • Including gravity in a short collision of a few milliseconds the impulse of gravity mgΔt is negligible.
Long interactions
  • Long interactions a rocket firing or a person jumping must include weight in the net force.
Single force
  • Single force the impulse of one force can be stated if clearly identified.
    • (floor on a jumper)
Direction
  • Direction a ball struck by a bat gets impulse along the bat's push, generally opposite to the incoming direction.

Part 4 of 7Applications to safety

Applications to safety
Crumple zones, seat belts, airbags
  • Crumple zones, seat belts, airbags reduce Favg on a passenger by increasing the collision time while the impulse is constant.
Energy view
  • Energy view they also increase the distance over which kinetic energy is dissipated.
    • (work–energy theorem)
Crash mat
  • Crash mat lengthens the stopping time and reduces the force without changing the momentum change or the kinetic energy lost.

Part 5 of 7Impulse versus work

QuantityForce multiplied byChangesType
ImpulseTimeMomentumVector
WorkDisplacementKinetic energyScalar
Impulse versus work
Wall stopping a ball
  • Wall stopping a ball gives an impulse, but the wall's contact point does not move so it does no work.
Centripetal force
  • Centripetal force changes the direction of momentum, so it has an impulse, but does no work.
Separate conservation laws
  • Separate conservation laws momentum conservation uses forces over time;
    • energy conservation depends on energy transferred to thermal and other forms.

Part 6 of 7Units check

Force
  • 1 N = 1 kg·m/s2.
Impulse
  • 1 N·s = 1 kg·m/s.
Size check
  • 10 N for 1 s gives 10 N·s, enough to change a 1 kg object's speed by 10 m/s.

Part 7 of 7More from the specification

1Impulse analysis along an inclined slope
  • Impulse analysis along an inclined slope resolving force components along an inclined slope determines net momentum change in a trolley system.
2Inertia
  • Resistance of an object to changes in its motion.
3Force-time graph
  • A graph whose area is the impulse.
4External force
  • Force from the surroundings.
5Initial velocity
  • Velocity at the start, u.
6Linear momentum
  • The product of mass and velocity.
7Final velocity
  • Velocity at the end, v.
8Velocity
  • Rate of change of displacement.

Key terms

TermMeaning
ImpulseNet force times time, J = FΔt, equal to the change in momentum.
N·sSI unit of impulse, equal to kg·m/s.
Average forceConstant force that would give the same impulse in the same time.
Peak forceLargest instantaneous force during an interaction.

Avoid these mistakes

1
Confusing impulse with force — impulse is force multiplied by time.
2
Ignoring the direction of the impulse, which is the direction of the net force.
3
Using the peak force instead of the average force in J = FΔt.
4
Forgetting that N·s and kg·m/s are the same unit.
5
Thinking impulse needs a displacement as work does.

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