Turn on thread page Beta
    • Thread Starter
    Offline

    10
    ReputationRep:
    Hey! Anyone know how I might go about part a of this question?
    Offline

    11
    ReputationRep:
    (Original post by marinacalder)
    Hey! Anyone know how I might go about part a of this question?
    What question?
    Offline

    20
    ReputationRep:
    the lamina is folded too tightly to see :teehee:
    • Thread Starter
    Offline

    10
    ReputationRep:
    OMG!! hahaha!

    wow.. that pun... :lol::lol::lol:

    Name:  IMG_2093.jpg
Views: 103
Size:  489.5 KB
    Offline

    11
    ReputationRep:
    (Original post by marinacalder)
    ...
    1) Find the c-o-m C relative to S by treating it as a rectangle of uniform density \rho and triangle of uniform density 2\rho.

    2) When it hangs in equilibirum, then C is vertically underneath S. It's just geometry/trig thereafter.
    Offline

    19
    ReputationRep:
    (Original post by marinacalder)
    Name:  IMG_2093.jpg
Views: 103
Size:  489.5 KB
    6 a) Folding reflects the triangle in the dotted line, so R lies on PQ axis, vert below T. RT is vert, RQ horiz, both length 3. Vertices at R(1, 0), Q(4, 0), T(1, 3).

    A rectangle of h = 3, w = 1, density p, joins the triangle of density 2p along RT (identical triangle lies beneath).

    Area (r) = 3 x 1 = 3 => Mass (r) = 3p. Area (t) = 0.5 x 3 x 4 = 6 => Mass (t) = 12p. Mass (lamina) = 15p.

    com (r) is (0.5, 1.5). com (t) = mean of vertices' (x, y) coords: x_t = (1 + 1 + 4)/3 = 2, y_t = (3 + 0 + 0)/3 = 1.

    For (X, Y) coords of com (lamina):

    (15p)X = (3p)(0.5) + (12p)(2) = 3p/2 + 24p = 51p/2
    => X = 51/30 = 17/10

    (15p)Y = (3p)(1.5) + (12p)(1) = 9p/2 + 12p = 33p/2
    => Y = 33/30 = 11/10

    com (lamina) is 17/10 units from PS, 11/10 from PQ.

    b) If you hang the lamina from S, the line joining S to com (lamina) is the vert. Use R-A triangle to calc @:
    opp = X = 17/10, adj = PS - Y = 3 - 11/10 = 19/10.

    So [email protected] = (17/10)/(19/10) = 17/19 => @ = 41.8°
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: July 14, 2017
Poll
“Yanny” or “Laurel”
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.