What is an ideal pulley?

An ideal pulley is considered to be weightless and frictionless. It may change the direction of the force applied through the string but does not affect the tension in the string.

What are the properties of an ideal string?

An ideal string is massless and inextensible, meaning it has no mass and cannot stretch.

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Pulley

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Pulley

Ideal pulley is considered weightless and frictionless.

Ideal string is massless and inextensible.

The pulley may change the direction of force in the string but not the tension.

The only function of pulley (Which has no friction on its axle to retard rotation) is to change the direction of the cord that joins the two block

1.0Cases of Pulley

Case I

m₁ = m₂ = m

Tension in the string,

T = mg

Acceleration 'a' = zero

Reaction at the suspension of the pulley

R = 2T = 2 mg

Case II

m₁ > m₂

now for mass m₁,

m₁ g – T = m₁a .........(i)

for mass m₂

T – m₂ g = m₂ a .........(ii)

Adding (i) and (ii), we get

$a = \frac{( m _{1} - m _{2} )}{( m _{1} + m _{2} )} g and T = \frac{2 m _{1} m _{2}}{( m _{1} + m _{2} )} g$

$acceleration = \frac{net pulling force}{total mass to be pulled}$

$Tension = \frac{2 \times Product of masses}{Sum of two masses} g$

Reaction at the suspension of pulley R = $2 T = \frac{4 m _{1} m _{2} g}{( m _{1} + m _{2} )}$

Case III

For mass m₁ : T = m₁ a .........(i)

For mass m₂ : m₂g – T = m₂a . ........(ii)

Solving (i) and (ii), we get

$a = \frac{m _{2} g}{( m _{1} + m _{2} )} and T = \frac{m _{1} m _{2}}{( m _{1} + m _{2} )} g$

Case IV

(m₁ > m₂)

m₁g – T₁ = m₁a .........(i)

T₂ – m₂g = m₂a .........(ii)

T₁ – T₂ = Ma .........(iii)

by (i), (ii) and (iii)

$a = \frac{( m _{1} - m _{2} )}{( m _{1} + m _{2} + M )} g$

Case V

Mass suspended over a pulley from another mass on an inclined plane.

For mass m₁ : m₁g – T = m₁ a

For mass m₂ : T – m₂g sinθ = m₂a

acceleration

$a = \frac{( m _{1} - m _{2} s i n θ )}{( m _{1} + m _{2} )} g$

and

$T = \frac{m _{1} m _{2} ( 1 + s i n θ )}{( m _{1} + m _{2} )} g$

Case VI

For mass m₁ : T₁ – m₁g = m₁a

For mass m₂ : m₂g + T₂ – T₁ = m₂a

For mass m₃ : m₃g – T₂ = m₃a

$a = \frac{( m _{2} + m _{3} - m _{1} )}{( m _{1} + m _{2} + m _{3} )} g$

we can calculate tensions T₁ and T₂ from above equations.

2.0Also Read

Galaxies	Moon	Centripetal Force
Eclipse	Solar Eclipse	Magnets
Star	Rainbow	Velocity

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Pulley

Ideal pulley is considered weightless and frictionless.

Ideal string is massless and inextensible.

The pulley may change the direction of force in the string but not the tension.

The only function of pulley (Which has no friction on its axle to retard rotation) is to change the direction of the cord that joins the two block