Reply To: 2021 Section B Q9a

[Man Lam]

#8504

I asked a friend who is an retired engineer. His Ph.D. project was in string theory. I think it is worth to share his comments in here.

Message 1.
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Hi Man Lam,

I hope you are well.

I think I see what the examiner is getting at.
As you say v^2 = u^2 + 2as comes from conservation of energy.
After all it just derives from the integral of the force in the direction of motion over distance.

However, the examiner wishes to draw the distinction that the ‘a’ experienced by the cart is not constant, as you noticed.
I.e. What is ‘a’ of this equation in this problem?

Now, energy conservation means that however you slice and dice it, you will get the right values.

Nevertheless, I agree with the examiner preferring demonstration that the understanding of the problem is in terms of CoE against
using the other equation in which the meaning of the terms in this context is unclear.

Kind regards,

Keith.

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Message 2
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Hi Man Lam,

To be more succinct, in the equation

v^2 = u^2 + 2as

‘a’ represents a constant acceleration over a distance ‘s’.
At no point is the truck subject to an acceleration ‘g’.

If a body were to be falling freely, then certainly a = g and s = h.

One could therefore:
– apply the equation to a freely falling body.
– Note that in the rolling truck case with negligible friction the speed would have to be the same as for the falling body to conserve energy.

[And strictly, we also need to assume that the wheels of the trolley are also of negligible mass.]

I can’t really speak for examiners or teachers, but if a student uses an equation in a context to which it does not obviously apply,
then they ought to include the explanation as to why it can in fact be used if they are to be credited with understanding the actual physics.

Regards,

Keith