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Momentum and impulse

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Intros
Lessons
  1. Introduction to impulse and momentum:
  2. What is impulse?
  3. Derivation of impulse from Newton's second law
  4. Impulse equations, units
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Examples
Lessons
  1. Impulse = F⃗\bold{\vec{F}} ∙ Δt=Δp⃗\bold{\Delta t = \Delta \vec{p}}
    1. 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.
    2. 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.
    3. 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 = F⃗\bold{\vec{F}} ∙ Δt=m(v⃗f−v⃗i)\bold{\Delta t = m(\vec{v}_f - \vec{v}_i )}
    1. 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?
    2. 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?
    3. 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.
    4. 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?
    5. 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?
    1. Impulse = area under F  vs  t\bold{F\;\mathrm{vs}\; t} graph, during the time interval Δt \bold{\Delta t}
      1. 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
      2. 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
      3. 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
    2. Momentum and Impulse in two dimensions
      1. 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?
      2. 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?
      3. 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?
    Topic Notes
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    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

    p⃗=mv⃗\vec{p} = m \vec{v}

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

    m:m: mass, in kilograms (kg)

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


    Impulse

    J⃗=F⃗Δt=Δp⃗=m(v⃗f−v⃗i\vec{J} = \vec{F} \Delta t = \Delta \vec{p} = m( \vec{v}_f - \vec{v}_i)

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

    F⃗:\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)

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