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Physics Olympiads Problem#6


Fisikastudycenter.com-Physics Olympiads Problems and Solutions Examples.

Soal #6
A boy of mass 60 kg climbs 3 m along the ABC ladder.

Image

By ignoring the mass of the ladder, find the tension in the tie-rod, use the acceleration due to gravity g = 10 m/s2 .
(Sumber Soal: Fisikastudycenter.com-Modification of Soal OSN 2007 Indonesian-Kabupaten)

Solution
Draw the forces acting on the system:
Image

Σ Fy = 0
NA + NB = mg
NA + NB = (60)(10)
NA + NB = 600 ….(Equation 1)

Isolate parts of the ladder (AC and BC) then apply the equilibrium conditions:

Image
leftside (AC):
Σ τC = 0
−NA(1) − mg(0,25) −T(√15/2) = 0
−NA − (10)(60)(0,25) −T(√15/2) = 0
−NA − 150 − (√15/2) T = 0
NA = 150 + (√15/2) T ….(Equation 2)

rightside (BC):
Σ τC = 0
−NB(1) + T(√15/2) = 0
−NB + (√15/2) T = 0
NB = (√15/2) T…..(Equation 3)

Combine equation 1, 2 and 3:
NA + NB = 600
{ 150 + (√15/2) T} + {(√15/2) T} = 600
√15 T = 450
T = 450/√15 = 30√15 Newton

prepared By: Fisika Study Center
Literature:
-Soal OSN Fisika 2007
http://www.tofi.or.id
(Sumber:physics.fisikastudycenter.com)

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