Science Vault - Year 11 HSC Physics

8.4 - Moving About

8.4.4 - Momentum

momentum / impulse / conservation of momentum

Momentum

Momentum is defined as the mass of an object multiplied by the velocity.

p= mv

Since the momentum depends on the velocity, it is also a vector quantity. The units for momentum are kg.m.s-1 or Ns.

Momentum can also be described in terms of Newon's Second Law. If we measure the momentum of an object over a small period of time.

Since (v - u) / t = acceleration

F = ma

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Impulse

Taking the time to the left-hand-side of the equation above,

Ft = mv - mu

The force multiplied by the time has a special name, the impulse. The impulse is the change in the momentum. Impulse is a vector with units of kg.m.s-1 or Ns.

Impulse is the force multiplied by time the force acts on an object.

Impulse = Ft = Δp

Consider a ball that is thrown into the air. We can make the ball go higher in two ways, firstly, we can apply a larger force, F or we can make the same force act on the ball for a longer time.

If the force acting on the object is not constant over the time for the time in which the force acts, the impulse is given by the integral of the force with respect to time.

In collisions between moving objects, the magnitude of the impulse is what changes each object's velocity.

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Conservation of Momentum

Conservation is an important principle in physics in that it allows us to determine what happens in collisions or explosions. If a body A of mass mA and velocity u A collides with another body B of mass mB and velocity u B moving in the same direction. If A exerts a force F to the right on B for a time t then by Newton's third law, body B will exert an equal and opposite force to the left on A also for a time t but to the left. Thus the bodies receive equal but opposite impulse Ft. The changes of momentum must be equal and opposite. Therefore, the total momentum change is zero. In other words, the total momentum of A and B together remains constant. In mathematical terms:

mAuA+ mBuB = mAvA+ mBvB

This is the general case. For motion in 1-dimension, we can consider the momenta in one direction only which allows us to drop the vector notation and use positive and neagtive signs.

It is important to release that the momentum is conserved only when there are no external agent acting on the system that could add momentum to the system. They must be included in the system before the conservation of momentum can be applied.

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download worksheet 8.4.4.A - momentum

download worksheet 8.4.4.B - collisions

download experiment 7 - consveration of momentum

 
References

Syllabus References

These references relate to the content covered on this page and can be found in Section 8.4.4 of the syllabus.

4. Change of momentum relates to the forces acting on the driver of a vehicle.

Students learn to:

  • Define momentum as:

    p=mv.

  • Define impulse as the product of force and time.

  • Explain why momentum is conserved in collisions in terms of Newton’s Third Law of motion.

Students:

  • Solve problems and analyse secondary data using:

    p=mv

    and

    Imulse=Ft

  • Perform first-hand investigations to gather data and analyse the change in momentum during collisions.

  • Solve problems that apply the principle of conservation of momentum to qualitatively and quantitatively describe the collision of a moving vehicle with:

    – a stationary vehicle
    – an immoveable object
    – another vehicle moving in the opposite direction
    – another vehicle moving in the same direction

Textbook References

Taken from:

Heffernan, D., Parker, A., Pinniger, G. & Harding, J. (2002) Physics Contexts 1, Pearson Education, Melbourne

  • Section 2.6 on pp. 78 - 87