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Turning effects

All objects have different forces acting on them. If an object is not moving, it has a total net force of zero (Newton's Second Law of Motion). Moments describe how forces are applied with respect to an axis of rotation. This is created by the fact that the reaction force pushing up on the object due to its weight may not be in the same place as an applied force. The system created by the object, the pivoting point (fulcrum) and the applied force will rotate in the direction of the net force. To remain in equilibrium the system requires a second force counterbalancing the first force.

Torque on a shelf
Torque is the measure of moment of force, and is proportional to the perpendicular distance from the pivot point, or fulcrum

Two children on a seesaw is a good example of moments. Two equally weighted children must sit the same distance from the centre fulcrum in order to remain in equilibrium. If one of the children is joined by a friend, the two must move half way to the centre for the moment forces to balance out. This is because the moment force is equal to the applied force x the distance from the fulcrum.

Moment = F . d

Seesaw moments
A system in equilibrium will have forces cancelling each other out. In this case, M1 attempts to turn the system in a counter-clockwise direction, and M2 acts in the clockwise direction.

The turning action applied across a fulcrum is the torque, and its symbol is τ, and the unit is N.m

Levers

A lever enables people to lift heavy objects. A lever works by a long handle over a fulcrum close to the mass to be moved.

Archimedes, the famous Greek scientist who lived in the 3rd century BCE, is reputed to have said of levers: 'Give me a place to stand, and I will move the world'. Of course, without a fixed fulcrum, no lever would move anything.

A seesaw demonstrates the moments involved in levers
A lever allows a smaller mass to move a larger, if it is sufficiently far from the fulcrum.

He had discovered that if he wanted to move a heavy weight, placing a piece of wood under it, and creating a pivot point with a rock, he could make a lever, which made lifting a lot easier.

A lever makes use of the fact that the force applied increases the further it is from the pivot point, or fulcrum, causing a rotation movement. This force of moment is called torque.

Tools

Tools like hammers and spanners use force of moment, or torque, to apply greater force than would be otherwise possible.

A hammer is also a lever

The hammer can lever up a nail because the force applied to the handle is much further than the nail from the fulcrum point on the head.

A spanner is also an example of a tool which utilises the lever principle to good effect. Trying to turn a bolt with the fingers is impossible. But when we put a spanner on it, we find our arm has enough strength to cause the bolt to rotate. The longer the spanner the more force we can apply.

Another example of a lever is the seesaw. An adult can find equilibrium with a child by sitting closer to the central fulcrum.

The Maths

The moment of force, or torque, which is applied by a mass m1, at distance d1, is:

$$F⋅d_1 = m_1_⋅g⋅d$$

where d is the distance from the fulcrum.

The mass m2 at distance d2 that can be moved must be applying a torque to the lever in the opposite direction less than the torque of mass m1.

Content © Andrew Bone. All rights reserved. Created : December 18, 2013

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