Find an expression in terms of S1 and S2 for the magnitude of the resistance force

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TSR360
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#1
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Question: https://prnt.sc/rerhdk
My working out: https://prnt.sc/rftqja
Answer in textbook: https://prnt.sc/reroyg


I've been stuck on this Q for hours, the closest form I could get to the solution in the textbook is by using a d-t graph which gives me the speed instead of RF: https://prnt.sc/rfvsj7
Last edited by TSR360; 1 year ago
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ghostwalker
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(Original post by TSR360)
Question: https://prnt.sc/rerhdk
My working out: https://prnt.sc/rftqja
Answer in textbook: https://prnt.sc/reroyg


I've been stuck on this Q for hours, the closest form I could get to the solution in the textbook is by using a d-t graph which gives me the speed instead of RF: https://prnt.sc/rfvsj7
Well your distance time graph is going to be incorrect; we have constant deceleration, so velocity will be linear (a straight line), but displacement will be a curve (part of a quadratic in shape).

Your velocity time graph wants to start at a positive value and descend in a straight line. If it started at zero, there would be no resistive force as there's no motion.

You seem to assume that Sn is the distance travelled in the first n seconds. It's not, it's the distance travelled in the nth second, i.e. from time, t=n-1 to t=n.

PS: Agree with their answer.
Last edited by ghostwalker; 1 year ago
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TSR360
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(Original post by ghostwalker)
Well your distance time graph is going to be incorrect; we have constant deceleration, so velocity will be linear (a straight line), but displacement will be a curve (part of a quadratic in shape).

Your velocity time graph wants to start at a positive value and descend in a straight line. If it started at zero, there would be no resistive force as there's no motion.

You seem to assume that Sn is the distance travelled in the first n seconds. It's not, it's the distance travelled in the nth second, i.e. from time, t=n-1 to t=n.

PS: Agree with their answer.
I still get the wrong answer: www.prnt.sc/rgphs4
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ghostwalker
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(Original post by TSR360)
I still get the wrong answer: www.prnt.sc/rgphs4
You want to do S1-Sn, rather than S1+Sn, in order to eliminate the u.
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TSR360
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(Original post by ghostwalker)
You want to do S1-Sn, rather than S1+Sn, in order to eliminate the u.
Thanks. But even with the u, isn’t it technically correct? The question didn’t ask me to simplify my answer.
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ghostwalker
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(Original post by TSR360)
Thanks. But even with the u, isn’t it technically correct? The question didn’t ask me to simplify my answer.
Well it asked for the force in terms of S1 and Sn. Having an extra unknown in there is certainly not in the spirit of the question.

If this were an experiment and you're given S1 and Sn (and implicitly n), you can't use your formula to work out the force.
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