Forces, Motion, & Energy - Lesson 8 Notes

Forces, Motion, & Energy

  • Year 10 Physics
  • Lesson 8 focuses on:
    • Explaining changes in momentum as caused by a net force: \Delta p = F_{net} \Delta t
    • Analysing impulse in an isolated system (collisions between objects moving in a straight line): F \Delta t = m \Delta v
    • Investigating and analysing momentum theoretically and practically.
  • Area of Study 1

Goal and Success Criteria

  • Goal: Describe momentum of moving objects and analyse changes in momentum during collisions.
  • Success Criteria:
    • Describe momentum quantitatively and qualitatively.
    • Calculate the impulse on an object during a collision.
    • Apply the theory of conservation of momentum to two objects colliding in a closed system.
  • Question: Why do cars crumple & airbags explode?

Key Vocabulary

  • Momentum
  • Conservation of Momentum
  • Mass
  • Velocity
  • Impulse

Crumple Zones

  • Crumple zones are a structural safety feature in vehicles.
  • They increase the time over which a change in velocity (and consequently momentum) occurs during a collision through controlled deformation.

Air Bags

  • Sensors detect abrupt deceleration during an accident.
  • A signal is sent to a heating element in the airbag circuit, causing a small explosion.
  • This explosion rapidly fills the nylon airbag with gas, expanding it to act as a cushion.
  • Chemical reaction: 2 NaN3 \rightarrow 2 Na + 3 N2
  • 130 grams of sodium azide produces 67 liters of nitrogen gas, sufficient to inflate a normal airbag.

Momentum

  • All objects with mass, if moving, have momentum.
  • Momentum depends on:
    • How much "stuff" (mass) is moving.
    • How fast the "stuff" is moving (velocity).

Momentum Example

  • Truck vs. Sports Car:
    • If a truck and a sports car are traveling at the same speed, the truck has more momentum due to its larger mass.
  • Police Car vs. Escape Vehicle:
    • If a police car and an escape vehicle have the same mass, but the police car is catching up, the police car has more momentum because it has higher velocity.
  • Collision Scenario:
    • Question: Would you rather be in a collision with a sprinter (mass: 65 kg, speed: 7 ms-1) or a rugby player (mass: 91 kg, speed: 5 ms-1)?

Momentum Equation

  • Momentum (p) is calculated as: p = mv
    • p = momentum (kg ms-1)
    • m = mass (kg)
    • v = velocity (ms-1)

Momentum Example (Continued)

  • Sprinter:
    • Mass = 65 kg
    • Speed = 7 ms-1
    • Momentum = 455 kg ms-1
  • Rugby Player:
    • Mass = 91 kg
    • Speed = 5 ms-1
    • Momentum = 455 kg ms-1
    • In this specific scenario, the momentum is the same for both.

Momentum vs. Inertia

  • Similarities:
    • Both relate to an object's resistance to changes in motion.
  • Key Differences:
    • Momentum is quantitative (assignable value), while inertia is qualitative (describable with words).
    • A stationary object has zero momentum but still possesses inertia.

Momentum Calculation Examples

  • Example 1: Calculate the momentum of a 65.0 kg student walking at 3.50 ms-1 east.
  • Example 2: Calculate the mass of a car driving at 16.7 ms-1 north with a momentum of 20 500 kg ms-1.

Impulse

  • Impulse refers to a fast-acting force or impact.
  • Defined as the sudden force acting on an object for a short interval of time.
  • Impulse is equal to the change in momentum of an object.
  • Impulse is also equal to the net force applied on an object multiplied by the duration the force is applied.

Impulse Equations

  • J = \Delta p
    • J = impulse
    • \Delta p = change in momentum (kg ms-1)
  • J = F_{net} \times \Delta t
    • F_{net} = Net force (N)
    • \Delta t = change in time (s)
  • Remember: \Delta = change = final - initial

Force-Time Graph for Impulse

  • A force-time graph shows the relationship between the force applied to an object and the time over which it is applied.
  • The y-axis represents force (F) in Newtons (N), and the x-axis represents time (t) in seconds (s).
  • The area under the curve of a force versus time graph represents the impulse delivered to an object.

Impulse and Collision Time

  • For any collision with a fixed change in momentum, if the time of contact is increased, the peak force is reduced.

Impulse and Newton's Second Law

  • F_{net} = ma = m \frac{\Delta v}{\Delta t}
  • F_{net} \times \Delta t = m \times \Delta v
  • F_{net} = \frac{\Delta p}{\Delta t}
    • Where:
      • F_{net} = Net force (N)
      • m = mass of the object (kg)
      • a = acceleration (ms-2)
      • v = velocity (ms-1)
      • t = time (s)
      • p = momentum (kg ms-1)
      • \Delta = change = final - initial

Impulse Calculation Examples

  • Example 3: Calculate the impulse of a 9.50 kg dog that changes its velocity from 2.5 ms-1 north to 6.25 ms-1 south.
  • Example 4: The momentum of a ball of mass 125g changes by 0.075 kg ms-1 south. If its initial velocity was 3.00 ms-1 north, what is its final velocity?
  • Example 5: A 45.0 kg mass changes its velocity from 2.45 ms-1 east to 12.5 ms-1 east in a period of 3.50 s.
    • Calculate the change in momentum of the mass.
    • Calculate the impulse of the mass.
    • Calculate the force that causes the impulse of the mass.
  • Extension: A student drops a 105g pool ball onto a concrete floor from a height of 2.00m. Just before it hits the floor, the velocity of the ball is 6.26 ms-1 down. Before it bounces back up, there is an instant in time where its velocity is zero. The time it takes for the ball to change its velocity is 5.02 milliseconds.
    • Calculate the impulse of the pool ball.
    • Calculate the average net force that acts to cause the impulse.

Conservation of Momentum

  • Momentum is conserved in an interaction or collision between objects.
  • The total momentum before a collision equals the total momentum after the collision in a closed system.

Conservation of Momentum Equation

  • \Sigma pi = \Sigma pf
  • m1u1 + m2u2 = m1v1 + m2v2
    • Where:
      • p = momentum (kg ms-1)
      • m = mass of the object (kg)
      • u = initial velocity (ms-1)
      • v = final velocity (ms-1)

Conservation of Momentum Examples

  • Example 6: Ball A (2.0 kg, 2.0 ms-1 west) collides with Ball B (4.0 kg, 1.0 ms-1 west). After the collision, Ball A moves westward at 1.0 m/s. What is the velocity of Ball B after the collision?
  • Example 7: A 0.50 kg ball at 6.0 ms-1 east collides head-on with a 1.00 kg ball at 12.0 ms-1 west. After the collision, the 0.50 kg ball moves away at 14 ms-1 west. Find the velocity of the second ball after the collision.
  • Example 8: A railroad car (30 000 kg, 2.2 ms-1 east) collides with another railroad car (30 000 kg) at rest. If they stick together, what is the velocity of the two cars?

Practice Questions

  • Choose your Goldilocks questions:
    • Discover: I need to practice.
    • Develop: I’m starting to get it.
    • Deepen: I’m ready for a challenge.
  • Instructions:
    • Choose a level that's not too easy or too hard.
    • Start at one level and adjust as needed.
    • Write out the question and answer, including all working.
    • Remember to include the equation and full substitution for full marks.

Your Turn - Questions

  • Discover

    • Question 1: A 5 kg bowling ball is rolled with a velocity of 10 ms-1. What is its momentum?
    • Question 2: A 155g baseball is incoming at a velocity of 25 ms-1 towards the batter… What is the magnitude of the impulse acting on the ball during the hit?

  • Develop

    • Question 1: Determine the momentum of: a 110 kg professional fullback running across the line at 9.2 ms-1, a 360 000 kg passenger plane taxiing down a runway at 1.5 ms-1.
    • Question 2: Calculate the momentum of a 110 kg football player running at 8.0 ms-1 Compare the player’s momentum with the momentum of a 0.410 kg football thrown hard at a speed of 25 ms-1

Review

  • Explain how crumple zones or airbags keep people safe in a car crash.