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Momentum explosions help please

Hi, im reading my text book and there is a paragraph I dont seem to understand :frown:

There are two trolleys (A&B) a spring is released from one of the trolleys, the two trolleys, A and B, push each other apart. (I GET THIS BIT)

There are blocks positioned so that the trolleys hit the blocks at the same moment. (I GET THIS BIT)

The distance travelled by each trolley to the point of impact with the block is equal to its speed x the time taken to travel that distance. (I GET THIS BIT)

As the time taken is the same for the two trolleys, the distance ratio is the same as the speed ratio. ( WHAT DO THEY MEAN BY THE DISTANCE RATIO BEING THE SAME AS THE SPEED RATIO ? WHAT IS THE DISTANCE AND SPEED RATIO ? )

Because the trolleys have equal (and opposite) amounts of momentum, the ratio of their speeds is the inverse of the mass ratio. ( I DONT UNDERSTAND THIS LINE ONE BIT)

The distance ratio should therefore be equal to the inverse of the mass ratio. ( DONT UNDERSTAND AGAIN)

In other words, if trolley A travels twice as far as trolley B, then the mass of A must be half the mass of B ( so they carry away equal amounts of momentum). (DONT UNDERSTAND)

Please help ! Thanks
Original post by Olive123


As the time taken is the same for the two trolleys, the distance ratio is the same as the speed ratio. ( WHAT DO THEY MEAN BY THE DISTANCE RATIO BEING THE SAME AS THE SPEED RATIO ? WHAT IS THE DISTANCE AND SPEED RATIO ? )

If I walk one way at 5 mph and you walk the other way at 10 mph
In one hour you walk twice as far as I do.
The distance ratio is 10 miles to 5 miles (or 2 to 1) and the speed ratio was 10mph to 5mph (or 2 to 1)


Because the trolleys have equal (and opposite) amounts of momentum, the ratio of their speeds is the inverse of the mass ratio. ( I DONT UNDERSTAND THIS LINE ONE BIT)

Conservation of momentum means that
m1v1 = m2v2 where m1 and m2 are the masses and v1 and v2 the speeds.
Simple maths gives
m1/m2 = v2/v1

The distance ratio should therefore be equal to the inverse of the mass ratio. ( DONT UNDERSTAND AGAIN)

If distance is proportional to speed (as shown in the 1st part), what happens if you put distance = kv in the mass ratio equation? (k is a constant of proportionality)
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Olive123
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Original post by Stonebridge
If I walk one way at 5 mph and you walk the other way at 10 mph
In one hour you walk twice as far as I do.
The distance ratio is 10 miles to 5 miles (or 2 to 1) and the speed ratio was 10mph to 5mph (or 2 to 1)


Conservation of momentum means that
m1v1 = m2v2 where m1 and m2 are the masses and v1 and v2 the speeds.
Simple maths gives
m1/m2 = v2/v1

If distance is proportional to speed (as shown in the 1st part), what happens if you put distance = kv in the mass ratio equation? (k is a constant of proportionality)


Thank you very much !!!! :smile:

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