AQA Physics PHYA4 - Thursday 11th June 2015 [Exam Discussion Thread]

I would say B: Clearly momentum doesn't change. For the kinetic energy, we know that the collision will slow down their overall speed (clearly they can't travel together at more than or equal to the speed of the first car!). But their mass is increased. kinetic energy is proportional to mv^2, where m gets bigger and v gets smaller, as we just showed. But v is squared, so v getting smaller causes more affect overall, so mv^2 get smaller overall. Hence the kinetic energy decreases. So: momentum is unchanged, kinetic energy decreases --> option B.

Omg I remember thinking this when I first did this question 😁😁

Thanks for reminding me!! I'm sure there will be a more logical way of doing it but I'm happy with that

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Reply 2821

gcsestuff

2

It's quite confusing if you do it in a mechanics maths way. That's obviously why they don't use numbers with it

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Reply 2822

a.a.k

2

Original post by gcsestuff

It's quite confusing if you do it in a mechanics maths way. That's obviously why they don't use numbers with it

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I am good with numbers i dont like ratii and when something is proportional to tbe other etc

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Reply 2823

Absent Agent

21

Original post by a.a.k

I am good with numbers i dont like ratii and when something is proportional to tbe other etc

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Both come from the same thing. I prefer neither. Before the mathematics of it is derived you have got to use your reasoning then to derive the mathematics of it. Unfortunately the education goes the other round

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Reply 2824

a.a.k

2

Original post by Mehrdad jafari

Both come from the same thing. I prefer neither. Before the mathematics of it is derived you have got to use your reasoning then to derive the mathematics of it. Unfortunately the education goes the other round

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Well i am not good with reason but facts

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Reply 2825

Absent Agent

21

Original post by a.a.k

Well i am not good with reason but facts

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Facts are obtained by the process of reasoning

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Reply 2826

Paul Dirac

2

Original post by a.a.k

I am good with numbers i dont like ratii and when something is proportional to tbe other etc

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Original post by gcsestuff

It's quite confusing if you do it in a mechanics maths way. That's obviously why they don't use numbers with it

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Not too hard actually, I just found a way to do it.

Let the mass of the first truck be m and let their combined mass be M. Let the speed of the first truck before the collision be v, and let their speed together after the collision V.

Momentum is conserved so mv=MV, i.e. V=mv/M.

Kinetic energy of first truck before collision: 0.5mv^2

Kinetic energy of both trucks together: 0.5MV^2=0.5M(mv/M)^2=0.5m^2v^2/M.

We want to find out which of these kinetic energies is larger.

First one is 0.5v^2*m, second is 0.5v^2(m^2/M), so we can ignore the factors of 0.5v^2 and concentrate on comparing the sizes of m and m^2/M. But M>m, because M=combined mass of m and the other truck. Therefore m^2/M<m^2/m=m. So the second kinetic energy is less than the first one, i.e. kinetic energy decreases.

Reply 2827

a.a.k

2

Original post by Mehrdad jafari

Facts are obtained by the process of reasoning

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Did i say before i wasnt good with words. I think did. Si plz excuse me i dont know what i am saying

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Reply 2828

gcsestuff

2

Original post by Paul Dirac

Not too hard actually, I just found a way to do it.

Let the mass of the first truck be m and let their combined mass be M. Let the speed of the first truck before the collision be v, and let their speed together after the collision V.

Momentum is conserved so mv=MV, i.e. V=mv/M.

Kinetic energy of first truck before collision: 0.5mv^2

Kinetic energy of both trucks together: 0.5MV^2=0.5M(mv/M)^2=0.5m^2v^2/M.

We want to find out which of these kinetic energies is larger.

First one is 0.5v^2*m, second is 0.5v^2(m^2/M), so we can ignore the factors of 0.5v^2 and concentrate on comparing the sizes of m and m^2/M. But M>m, because M=combined mass of m and the other truck. Therefore m^2/M<m^2/m=m. So the second kinetic energy is less than the first one, i.e. kinetic energy decreases.