# Equilibrium Principle of Moments

Can you please explain me some more problems on principle of moments, balancing see saw and forces acting on a bridge.

Would like to understand in such examples which forces are downward (CG)and upward.

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Q1- A fulcrum is created by balancing a ruler on a pencil as shown in figure below. Six pennies are placed at 10 cm to the left of the pivot point.

What is the torque (moment of the force) exerted by the stack of six pennies about the pivot point if each penny has a mass of 3 grams?

The torque is the rotational effect of a force and is given by the product of the force and perpendicular distance from the fulcrum.

Mass of the six pennies will be 6m = 6*3 gram = 18*10-3 kg

And thus their weight will be 6m*g = (18*10-3kg)*(10 m/s2) =18*10-2 N

Distance of six pennies from fulcrum d = 10 cm = 0.10 m

Hence the torque exerted about the pivot point will be

= 6mg*d = 18*10-2*0.10 = 1.8*10-2 Nm

This torque is anti-clockwise and hence taken as positive.

Answer: the torque of the six pennies will be 1.8*10-2 Nm anticlockwise.

If the ruler is to remain balanced, where do you need to place a stack of ten pennies?

To balance the ruler the net torque must be zero. For this the torque of the 10 pennies will be clockwise or they must be placed on the right side of the fulcrum so that it will be taken as negative and hence for balance

Net = 6mg*d - 10 mg* x = 0

Gives x = 6*d/10 = 6*10/10 = 6 cm.

Answer: for balance 10 pennies must be placed at 6 cm from the fulcrum to the right of the pivot point.

Q2

The torque is the rotational ...

#### Solution Summary

Four questions related to equilibrium of bodies and principle of moments are explained and solved.