Momentum and impulse

Momentum and impulse

Lessons

In this lesson, we will learn:

  • What is impulse?
  • Derivation of impulse from Newton's second law
  • Impulse equations, units
  • Problem solving with impulse and momentum
  • Problem solving with F vs t graph

Notes:

  • Impulse is change in an object's momentum.
  • To change an object's momentum, an impulse must be given to that object. An example would be kicking a soccer ball (an impulse) to set it into motion (give it momentum).
  • An impulse is defined as a force that acts on an object for a period of time.
  • In a graph of force vs. time, the area under the graph is impulse.

Momentum

p=mv\vec{p} = m \vec{v}

p:\vec{p}: momentum, in kilogram meters per second (kg∙m/s)

m:m: mass, in kilograms (kg)

v:\vec{v}: velocity, in meters per second (m/s)


Impulse

J=FΔt=Δp=m(vfvi\vec{J} = \vec{F} \Delta t = \Delta \vec{p} = m( \vec{v}_f - \vec{v}_i)

J:\vec{J}: impulse, in newton seconds (N∙s)

F:\vec{F}: net force acting on an object, in newtons (N)

Δt:\Delta t: the length of time for which the force acts, in seconds (s)

Δp:\Delta \vec{p}:change in momentum of an object, in kilogram meters per second (kg∙m/s)

  • Introduction
    Introduction to impulse and momentum:
    a)
    What is impulse?

    b)
    Derivation of impulse from Newton's second law

    c)
    Impulse equations, units


  • 1.
    Impulse = F\bold{\vec{F}}Δt=Δp\bold{\Delta t = \Delta \vec{p}}
    a)
    A tennis ball is initially at rest, then hit by a racket with 30.0 N [E]. The racket is in contact with the ball for 0.070 s. Find the impulse given to the ball by the racket, and the final momentum of the ball.

    b)
    A go kart has momentum 1000 kg·m/s forward when the engine applies a force of 55 N forwards for 6 s. Find the impulse given to the go kart by the engine and the final momentum of the go kart.

    c)
    A baseball is pitched with momentum 5.85 kg·m/s [S], and is hit by a bat which applies a force of 300 N [N]. The bat is in contact with the ball for 0.05 s. Find the impulse given to the ball and the final momentum of the ball.


  • 2.
    Impulse = F\bold{\vec{F}}Δt=m(vfvi)\bold{\Delta t = m(\vec{v}_f - \vec{v}_i )}
    a)
    A 1.25 kg skateboard rolls forward at 0.60 m/s. It is given a push forward with a force of 5.0 N for 1.2 s. What is the final velocity of the skateboard?

    b)
    A soccer ball is initially at rest. Kicking the ball with an impulse 1.30 N·s causes the ball to move at 3.00 m/s. What is the mass of the ball?

    c)
    A 0.035 kg rubber ball is thrown at a wall at 13 m/s and rebounds at 7 m/s. Find the impulse given to the ball by the wall.

    d)
    A 1200 kg car travels at 11 m/s [E]. At t = 5.0 s, the driver starts accelerating with a force of 300 N [E] applied to the car. If the final velocity of the car is 17 m/s, what is the time when the driver stops accelerating?

    e)
    A 50 kg ice skater glides without friction at 7.2 m/s [W] when he skates through a rough patch on the ice for 3.0 s. If his velocity after the patch is 4.5 m/s [W], what is the average force of friction experienced in the patch?


  • 3.
    Impulse of stopping a car

    A 1300 kg car travelling at 13.5 m/s [E] can be stopped in 20 s with gentle braking, 4.3 s in a panic stop, and 0.78 s if it hits a wall.

    1. What is the impulse given to the car to stop it in each case?
    2. What is the average force experienced by the car in each case?

  • 4.
    Impulse = area under Fvst\bold{F\;\mathrm{vs}\; t} graph, during the time interval Δt \bold{\Delta t}
    a)
    A 0.060 kg golf ball is struck by a golf club which exerts the force shown in the graph over a period of 0.001 s in the forward direction. Find the impulse exerted on the ball, and the final velocity of the ball.
    graph of golf ball F vs t

    b)
    b) A 0.425 kg soccer ball is moving 0.80 m/s [E] when it is kicked and experiences the force shown in the graph below. The direction of the kick is [W]. Find the final velocity of the ball.
    graph of soccer ball F vs t

    c)
    Two people begin pushing a cart. The force experienced by the cart is shown in the graph. At t = 5 s, person A lets go of the cart. At t = 12 s, person B lets go of the cart. Find the impulse person B gives the cart during the time he is the only person pushing it.
    graph of cart F vs t


  • 5.
    Momentum and Impulse in two dimensions
    a)
    a) A 1300 kg car travelling 12 m/s [W] is given a 1.6×104 N·s [N] impulse. What is the final velocity of the car?

    b)
    A 1.40 kg ball rolling 8.00 m/s [N] hits a barrier and bounces off, then moving 6.20 m/s [E]. What was the impulse given to the ball?

    c)
    A 0.25 kg billiard ball in motion is given an impulse of 0.78 N·s [E]. If the final velocity of the ball is 3.2 m/s [27° S of E], what was the initial velocity of the ball?