M3 Jan 05

Hi
Does anybody have the answers or even their own answers for this paper? I would be pleased if I could check mine with someone on here. Widowmaker would be good if he has done it :biggrin:

Reply 1

lgs98jonee

Simple numerical answers would be great...and also I cant do 2b....

Reply 2

Christophicus

lgs98jonee

Simple numerical answers would be great...and also I cant do 2b....

here I be.

M3 Jan 05
1)a T = 5.47N
1)b @ = 26°

2)a y-bar = 3(M-2m)r/8(M+m) as required
2)b M > 26m as required

3)a y-bar = π/8
3)b θ = 75.96°

4)a b = (2-√2)L
4)b v = L(π√2/3)
4)c t = 0.28s

5)a v = 30 - 6√(t+4) ms^-1
5)b x = 162m

6)a λ = 8mg/9
6)b a = -[8g/9L]x
6)c(i) Period = 3π√(L/2g)
6)c(ii) v_max = [5/4]√(2gL)

7)a v = 8ms^-1
7)b m = 6kg
7)c T = 1294N

These are my answers and they're all correct as I've checked them against a mark scheme.

Reply 3

lgs98jonee

Thanks....how do you do 2B?

Reply 4

lilbug

2b.
Lets call the midpoint of AB...M. And the centre of gravity G.
Find tan θ using the triangle AMO formed by the radius of the hemisphere and the height of the cone (i.e. OM).
tan θ = r/3r = 1/3
Then in the triangle AMG formed by the radius of the hemisphere and the distance y found in (a)
tan θ = y/r
If there is no equilibrium,
y/r > 1/3
(because the weight will no longer be acting within AO when tan θ exceeds its limit)
y > r/3
3(M-2m)r/8(M+m) > r/3
Solve to get
M > 26m.

Reply 5

lgs98jonee

I also get 5 B wrong :/

Reply 6

lilbug

5b.
integrate the answer you got in 5(a), as v=dx/dt
Substitute x=0, v=0 into it to get the value of C, and plug it back in.

Substitute v=0 into the 5(a) answer to find the value of t when P was at rest.
You should get t=21, which you then substitute into the displacement-time equation you formed before.
The answer is 162 m.
If you're still having problems, tell me and I'll show you my working-out in detail.