IB DP Physics: SL复习笔记2.4.4 Collisions & Explosions

Collisions & Explosions

  • In both collisions and explosions, momentum is always conserved
    • However, kinetic energy might not always be
  • A collision (or explosion) is either:
    • Elastic – if the kinetic energy is conserved
    • Inelastic – if the kinetic energy is not conserved
  • Collisions are when objects strike against each other
    • Elastic collisions are commonly those where objects colliding do not stick together and then move in opposite directions
    • Inelastic collisions are commonly those where objects collide and stick together after the collision

Elastic-Inelastic-Collisions

Elastic collisions are where two objects move in opposite directions. Inelastic collisions are where two objects stick together

  • An explosion is commonly to do with recoil
    • For example, a gun recoiling after shooting a bullet or an unstable nucleus emitting an alpha particle and a daughter nucleus
  • To find out whether a collision is elastic or inelastic, compare the kinetic energy before and after the collision
  • The equation for kinetic energy is:

5.2.4-Kinetic-energy-equation

Worked Example

Two similar spheres, each of mass m and velocity v are travelling towards each other. The spheres have a head-on elastic collision.What is the total kinetic energy after the impact?WE-Elastic-collision-question-image

WE-Elastic-collision-answer-image

Worked Example

Trolley A of mass 0.80 kg collides head-on with stationary trolley B at speed 3.0 m s–1. Trolley B has twice the mass of trolley A.The trolleys stick together and travel at a velocity of 1.0 m s–1.Determine whether this is an elastic or inelastic collision.

Collisions-Worked-Example-Answer-1Collisions-Worked-Example-Answer-2

Exam Tip

If an object is stationary or at rest, its velocity equals 0, therefore, the momentum and kinetic energy are also equal to 0When a collision occurs in which two objects are stuck together, treat the final object as a single object with a mass equal to the sum of the two individual objectsDespite velocity being a vector, kinetic energy is a scalar quantity and therefore will never include a minus sign - this is because in the kinetic energy formula, mass is scalar and the v2 will always give a positive value whether its a negative or positive velocity

Applying Conservation of Momentum

  • The principle of conservation of momentum can be used to solve various types of problems for isolated systems such as problems involving:
    • Collisions
    • Fluid jets
    • Conveyor belts
    • Explosions & many more
  • Kinetic energy can also be used to check if a collision is elastic or inelastic
    • In elastic collisions, momentum and kinetic energy are conserved
    • In inelastic collisions, momentum is conserved, but kinetic energy is not
    • Inelastic includes explosions

Worked Example

Two trolleys X and Y are of equal mass. Trolley X moves towards trolley Y which is initially stationary. After the collision, the trolleys join and move off together.Show that this collision is inelastic.

WE-Inelastic-collision-question-image

WE-Inelastic-collision-answer-image

Worked Example

A 2 kg crossbow is fired and a 100 g arrow is fired horizontally. The arrow is released from the crossbow at 40 m s−1.Determine the magnitude of the recoil velocity of the crossbow.2.4.4-Worked-Example-Crossbow-arrow-1

Step 1: List the known quantities

    • Mass of the crossbow: 2 kg
    • Mass of the arrow: 100 g = 0.1 kg
    • Speed of arrow during release: 40 m s−1

Step 2: Determine the momentum before release

    • Since before release neither the arrow nor the crossbow was moving, their momentum together is 0 kg m s−1

Step 3: Determine the momentum of the arrow

    • The momentum of the arrow can be found from the equation:

p = m × v

parrow = 0.1 × 40 = 4 kg m s−1

Step 4: Determine the recoil velocity of the crossbow

    • The arrow has a momentum of 4 kg m s−1 and the system had a total momentum of 0 kg m s−1 before the collision
    • Therefore, the crossbow must have a momentum of 4 kg m s−1 in the opposite direction to the arrow
    • Therefore:

pcrossbow = m × v

pcrossbow ÷ m = v

v = 4 ÷ 2 = 2 m/s in opposite direction to arrow

Step 5: State the final answer

    • The magnitude of the recoil velocity of the crossbow is 2 m s−1.

 

 

 

 

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