Momentum and its conservation

What is momentum?

Momentum is defined as the product of the mass of a body and its velocity. It is measured in kgms^-1 . It gives an idea of how much motion a body has and it can be used to predict what will happen it two or more bodies collide.

momentum = mass x velocity

p = m x v

Eg. 1 If a body of mass 5kg is moving at a speed of 4 ms^-1 , the total momentum of the moving body is

p = m x v

p = 5 kg x 4 ms^-1

p = 20 kgms^-1

Eg 2. If a body of mass 2kg is moving at a speed of 10 ms^-1 , the total momentum of the moving body is

p = m x v

p = 2 kg x 10 ms^-1

p = 20 kgms^-1

The principle of the conservation of momentum states that when two or more bodies act on one another as in a collision, the total momentum of the bodies remain constant, provided no external forces act (e.g friction).

Eg. 3

Use the principle of the conservation of momentum to solve for v.

Before collision total momentum = (17 kg x 2 ms_-1 + 5kg x 0) = 34 kgms^-1

^{Total momentum after = (17 kg + 5 kg) x v = 22v}

from the principle we can write that34 kgms^-1 = = 22v

v = 34 / 22 = 1.5 ms-1

Momentum is a vector so the direction that it acts in plays an important role.

Momentum is also conserved during explosions such as in the firing of a gun or in the release of a rocket. The total momentum before the explosion is equal to the total momentum after the explosion.

If a gun of mass 5 kg fires a bullet of mass 0.05 kg with a velocity of 300 ms^-1 , calculate the velocity at which the gun recoils.

The momentum of the fired bullet is 0.05 kg x 300 ms^-1 = 15 kgms^-1

Since the total momentum before explosion is zero the gun would have a backward momentum of the same amount.

Momentum of gun after firing = - 15 kgms^-1 (the negative sign indicates that the momentum is in the opposite direction to the bullet)^.

mv _(gun) ⁼ - 15 kgms-1

v = 15 / 5 = - 3ms^-1 or simply 3 ms^-1 in the opposite direction to the bullet.