The pulleys move

Classical Mechanics Level 4

The pulley block system is shown in the figure. All strings and pulleys are ideal. The relation between a 1 , a 2 , a 3 a_{1},a_{2} , a_{3} is given as x a 1 + y a 2 + z a 3 = 0 xa_{1}+ya_{2}+za_{3}=0 where x , y , z x,y,z are co prime integers. Find ∣ x + y + z ∣ |x+y+z| .


The answer is 10.

Tanishq Varshney by Tanishq Varshney , 23, India

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2 solutions

Satvik Pandey
Apr 9, 2015

By the concept of virtual work method we get

∑ T ⃗ a ⃗ = 0 \sum { \vec { T } \vec { a } =0 }

From the figure

− ( 2 T + T 2 ) a 1 − T 4 a 3 + T 4 a 2 = 0 -\left( 2T+\frac { T }{ 2 } \right) { a }_{ 1 }-\quad \frac { T }{ 4 } { a }_{ 3 }+\frac { T }{ 4 } { a }_{ 2 }=0

So − 10 a 1 + a 2 − a 3 = 0 -10{ a }_{ 1 }+{ a }_{ 2 }-{ a }_{ 3 }=0

So ∣ x + y + z ∣ = 10 \left| x+y+z \right| =10

17 Helpful 0 Interesting 0 Brilliant 0 Confused

Can you explain T/2 and T/4 part please?

Jayakumar Krishnan - 5 years, 9 months ago

Where did u come across this method,I referred many books of NLOM but never found this thing

Suneel Kumar - 4 years, 11 months ago
Atharva Sarage
Jun 13, 2015

Just use the concept-----. Work done by tension is 0.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Can u elaborate

Suneel Kumar - 4 years, 11 months ago

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