# Factors that affect work & The effect of the angle between force and displacement on work

**Work**

**The meaning of work in physics is different from that used in everyday life , Work does not mean that a tough task is done , In physics , there are two conditions for work to be done which are the acting force and the displacement in the direction of the force .**

**That can be illustrated by the following two examples :**

**The player who lifts weights up does work because the force acting on the weights moves them upwards through a distance in the direction of the force .**

**The person who pushes the wall does no work because the force acting on the wall fails to move it and the wall remains motionless .**

**So , when a force acts on an object to move it through a certain displacement in the direction of the force , it is said that the force does work .**

**Work done ( W ) is determined by the relation : W = F . d , Where ( F ) is the acting force and ( d ) is the displacement of the object along the line of the force action .**

**If the direction of the force ( F ) is inclined at an angle ( θ ) to the direction of displacement ( d ) , then , ****W = F d cos θ .
**

**The unit of measuring work is kg.m²/s² , which is equivalent to N.m or Joule ( J ) , Dimensions of work are ML²T ^{−2} . **

**Thus work and its unit Joule are defined as follows :**

**Work : It is the dot product of the acting force ( F ) and the displacement ( d ) in the direction of the force . **

**The Joule : It is the work done by a force of one Newton to move an object through a displacement of one meter in the direction of the force .**

**When a person does work of 200 J on an object , It means that when this person acts on the object by a force 200 N , the object is displaced through 1 m along the line of the force action .**

**Although both force and displacement are vector quantities , work is a scalar quantity because work is the dot product of the force and the displacement .**

**Factors that affect work**

**The acting force on the body : Work is directly proportional to the acting force at constant displacement and constant angle between force and displacement .**

**Slope = W / F = d cos θ**

**The displacement of the body : Work is directly proportional to the displacement at constant force and constant angle between force and displacement .**

**Slope = W / d = F cos θ**

**W = F d cos θ**

**The angle between the force and displacement : Work is directly proportional to cosine the angle between the force and the displacement at constant force and constant displacement . **

**Slope = W / cos θ = F d **

**The effect of the angle between force and displacement on work**

**When the angle between the force and displacement = zero , The work done is maximum when the direction of force is the same as the direction of displacement , such as a person pulling an object through a certain distance .**

**W = F d cos 0° = F d**

**When θ =90° , The work done is zero when the direction of force is perpendicular to the direction of displacement , W = F d cos 90° = 0 .**

**Example : A person moves horizontally while carrying an object where the horizontal displacement of the object is perpendicular to the direction of pulling .
**

**When 0 ≤ θ < 90° , Work done is positive , The person does work on the object , W = F d cos θ = + ve value .**

**Example :**** A person pulling an object . **

**When 180° ≤ θ < 90° , Work done is negative , The object does work on the person , W = F d cos θ = − ve value .
**

**Example :**** A person pulling an object while moving opposite to the direction of the force .**

**When θ =180° , Work done is negative , The direction of force is opposite to the direction of displacement , W = F d cos 180 = − F d .
**

**Example : The work done by the force of car brakes , The work done by the frictional forces .**

**Work done when pushing an object forwards is greater than dragging it behind , Because : On pushing , the force component ( F sin θ ) acts in the direction of the object weight ( w ) that increases friction , More work is required to move the object .**

**On dragging , The force component ( F sin θ ) acts opposite to the direction of the object weight ( w ) that decreases friction , Less work is required to move the object .**

**Finding work done graphically**

**Work done can be found graphically by using the ( force – displacement ) graph , If a constant force ( F ) acted on a body and displaced it through a displacement ( d ) in the direction of the force , θ = 0 .**

**When representing the relation ( force versus displacement ) graphically , we get a straight line parallel to displacement axis .**

**Work = Force × Displacement**

**Work ( graphically ) = Length × Width**

**Work = The area below the ( force – displacement ) curve .**

**James Joule ( 1818 – 1889 ) : An English scientist who was the first who realized that work generates heat , In one of his experiments , he found that water temperature at the bottom of a waterfall is higher than that at the top , concluding that a part of water energy is converted into heat .**

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