Question

Example 3 A person using a 40 cm long handled spanner can
open a nut by applying a 120 N force. What should be the length of
the handle if he wants to open the nut by applying a force of 30 N​

Answer 1

Answer:-

The length of the handle when applied force is 30 N is 1.6 m

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• Given:-

Length of handle [L1] = 40 cm → 0.4 m

Force applied [F1] = 120 N

Force applied [F2] = 30 N

• To Find:-

Length of the handle [L2] = ?

• Solution:-

Equating the Torque :-

$\boxed{\bf{F1 \: L1 = F2 \: L2}}$

• Putting in the Values:-

→ 120 × 0.4 = 30 × L2

→ 48 = 30 × L2

→ L2 = $\dfrac{48}{30}$

→ L2 = 1.6 m

Therefore, the length of the handle when Force of 30 N is applied will be 1.6 m

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Some Additional Information:-

➣ What is Torque?

• Torque is a force that can cause rotation in an object.

•The point where the object rotates is known as the axis of rotation.

• Torque has the dimension of force times distance, $\sf{M L^2T^{-2}}$

• S.I unit → kgm²s-²

• Mathematically, torque can be represented as τ = F.r. sinθ

• Unit if Torque → Newton-metre [Nm]

• Mainly denoted with the symbol the Greek letter tau, “τ”

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