1995 + 1996 Past HSC Mechanics questions (1 Viewer)

[u-borat]

If anyone could post a written solution to 1995 Q8c)iii) and 1996 Q6b), that'd be muchly appreciated.

 

[u-borat]

also help with this induction please?



1+ 1/2^2 + 1/3 +......+ 1/n^2 =< 2- 1/n

 

[Affinity]

helps if you post the questions.

for the 2nd one.. the key is to notice that

2 - 1/(n+1) > 2 - 1/n + 1/(n+1)^2
it's not that hard to prove by rearranging, noting that n(n+1) > (n+1)^2.

you can also prove the inequality by noting that the sum is less than

1+ integral[1 to n] 1/x^2 dx

by considering areas.

 

[fishbulb]

For 1996 6b)

Resolving forces tangentially and normally:
EFx = mrw^2 = F - mgCos0
Efy = 0 = mgSin0 + N

therefore F/N = (mrw^2 + mgCos0)/(-mgSin0)

= (rw^2 + gCos0)/(-gSin0)

check my solution, i did it really quickly