Forces and motion, Year 11: momentum

Momentum

HintIt is measured in kg m/s.

The whyIn symbols, p = m v, with p in kilogram metres per second, m in kilograms and v in metres per second. AQA expects this equation to be recalled. Because velocity has a direction, this quantity is a vector too.

540

HintMultiply the two numbers you have been given.

The whyMomentum = mass × velocity, p = m v = 60 × 9. The unit comes from multiplying the units: kilograms × metres per second gives kg m/s. The equation must be recalled.

15 m/s

HintRearrange the momentum equation so that velocity stands alone.

The whyp = m v rearranges to v = p ÷ m = 6 ÷ 0.4. Dividing by a number less than one makes the answer bigger: a light ball must move quickly to carry this much momentum.

+6 kg m/s and −6 kg m/s; the total is zero

HintGive the trolley moving to the left a negative velocity.

The whyMomentum is a vector, so direction matters. The trolley moving right has p = 2 × 3 = +6 kg m/s; the one moving left has p = 2 × (−3) = −6 kg m/s. Adding them gives zero, even though both trolleys are moving.

The tennis ball — the parked lorry has none

HintCheck the velocity of each before you look at the masses.

The whyMomentum = mass × velocity, so an object that is not moving has zero momentum however large its mass. Momentum is a property of moving objects only. The ball's momentum is tiny, but it is still more than nothing.

Conservation of momentum

HintThe rule for energy has the same first word: a total that never changes.

The whyAn 'event' is usually a collision or an explosion. Individual objects may speed up, slow down or reverse, but when every object's momentum is added together, with direction taken into account, the total is the same afterwards as before.

closed; equal

HintThe first describes a system that nothing outside is pushing or pulling on.

The whyA system of this kind is one on which no external forces act, so its objects affect only each other. Two trolleys on a low-friction track are close to this. If an outside force such as friction is significant, it changes the total momentum and the rule no longer holds exactly.

The total momentum must stay zero, so she gains momentum equal to the ball's but in the opposite direction

HintAdd up what is moving before the throw.

The whyBefore the throw neither the skater nor the ball is moving, so the total momentum is zero. Afterwards the ball has forward momentum, and the total can only still be zero if the skater has the same amount backwards. She has more mass than the ball, so she moves more slowly than it does.

The same total momentum is now shared by twice the mass

HintAsk how much more material is moving afterwards.

The whyTotal momentum is conserved in the collision. Before, all of it belonged to one trolley; afterwards the same amount is carried by two trolleys' worth of mass. With the mass doubled and momentum unchanged, the velocity must halve.

5 kg m/s to the right

HintFind the total before the collision, taking direction into account.

The whyTaking right as positive, the total before is 8 + (−3) = 5 kg m/s to the right. In a closed system the total momentum after an event equals the total before, so it is still 5 kg m/s to the right, however the two trolleys share it.