# Evan's Space

## Important Concepts on Moments

When a system is in equilibrium, 2 conditions are met.

1) Principle of Moment (POM):
Sum of anticlockwise moment = Sum of clockwise moment

2) Net force = 0N; all forces are balanced:
Total downward forces = Total upward forces

Whenever a force passed through the pivot point, that force will not create any moment as there is no perpendicular distance from the force to the pivot. Hence this force will not be included in the calculation of moments.

## Balancing Toys

Balancing toys always return to its original position as their centre of gravity (CG) are below the pivot (balancing) point. This kind of system will create a restoring moment which helps to return the system to its original position when displaced slightly.

Such systems are in stable equilibrium. Characteristic of such system is that when displaced, the CG rises.

## Physics of Construction Lifting Truck

1) Why are the 4 extended legs necessary?
This is to increase the area of base of the truck to increase the stability. From our theory, as long as the weight acting vertically downward from the centre of gravity is within the area of base, there will be a restoring moment to bring the truck back to its original position, hence increases its stability.

2) In what situation will the truck topple? (note the the centre of gravity (CG) of the truck is in general very low due to mass concentration at the base)
Basically, there are 2 situdation:
– if the load that is lifted is too heavy, the overall new CG of the truck and load might shift outside the area of base, hence causing the truck to topple. i.e. the clockwise moment created by the load is created than the anticlockwise moment created the weight of truck.
– If the angle of tilt is too much which increases the perpendicular distance from load to pivot. Likewise, the overall CG might be outside the area of base and there is a net clockwise moment.

3) What is the purpose of the metal plate underneath the legs?
The purpose is to increase the area of base. The whole weight of the truck is spread over the 4 legs. Since P = F/A, with a bigger base area, the pressure acting on the ground will be reduced. This is to minimise any damages done to the ground.

## Restoring moment

This Lego structure which Daniel and Danry made is ‘Stable equilibrium’

Characteristics of stable equilibrium:
– when displaced, centre of gravity (cg) rises.
– the weight of the basket will create a restoring moment which returns the basket to its original position.
– when at rest, the weight of CG is directly below the pivot.

Below is a brief explanation

## Minimum force to lift a drum over a step

Given that the mass of the drum is 20 kg. What is the minimum force, F, required to just movee th drum off the ground? (Assume uniform mass of drum and g = 10 N/kg)

Knowing the position of the pivot and identifying the perpendicular distance is important.

Consider the 3 variations of the same question as shown below.

Type 1: Very straight forward as the pivot is same level as the CG of the drum. Hence p

endicular distance is easy to identify.

Type 2: Using pythagoras theorem to find the necessary perpendicular distance.

Type 3: Using Toa, Cah and Soh to find the necessary perpendicular distance.

## Moments Question using Simultaneous Equations

A non-uniform plank weighing 300 N is set up as shown. The spring balance reads 160 N when a small boy stands at A and 760 N when he stands at B. (Note: Non-uniform plank means the CG of the plank is not at its centre)

a) Find the weight of the boy.
b) How far is the centre of gravity of the plank from point A?

Solutions:

a) 300 N and b) 6.67 m

Click on the video tutorial if you can’t derive the 2 equations.

## Turning Effect of Force

The force diagrams shows all the forces acting on a beam of length 3x. Which force system causes only rotational motion of the beam without any linear movement?

Solutions: Option B

One has to note that the beam does not have a fixed pivot which it can turn about.

Hence beam is free to move when the 4 forces are acting on it. To create only rotational motion (it will rotate about a fixed position (centre of beam)) only, there will not be any linear movement (the centre of beam moves away from its original centre regardless if it is rotating).

To create only rotational motion, the only possible way is when the beam rotates about its centre point. Hence resultant moment created by the forces is either clockwise or anticlockwise moment.

Taking moment about centre, you have to do calculation on Clockwise Moment and Anticlockwise Moment.

For B:  Taking moment about centre and consider length x as 1 m, left hand side of pivot, moment = 4 x 1.5 + 2 x 0.5 = 7Nm anticlockwise moment right hand side of pivot, Anticlockwise moment = 3 x 1.5 + 5 x 0.5 = 7Nm anticlockwise moment

Hence only system B is able to have rotational motion anticlockwise moment.

For e.g C: LHS of pivot, moment = 2 x 1.5 – 4 x 0.5 = 1Nm anticlockwise moment RHS of pivot, moment = 3 x 1.5 + 5 x 0.5 = 2Nm anticlockwise moment

Though system will rotate anticlockwise, but the anticlockwise moment on both sides are not equal , thus will cause linear movement.

Upward forces = downward forces does not mean body will be at rest.  Rather only if the body is at rest / moving at constant velocity, then the forces are balanced and resultant is zero. (Newton’s 1st law)