Different types of work done with an example each
Work: In physics work is said to be done when a force acting on a body displaces it through a certain distance. The work by a constant force is measured by the dot product of force will displacement.
i.e. W = F.S or W = F S cosθ …(1)
where F = force and S = displacement
And θ = angle between F and S.
From eq.(1), we have W=F cosθ S. Therefore, work done by a force is equal to the product of the component of the force in the direction of displacement of the body and the distance through which the body moves.
As work is the dot or scalar product of two vectors (force and displacement), therefore, it is a scalar quantity.
Special cases:
CaseI: When the body moves in the direction of the force. In this case, q = 0o.
from eq (i), we have
W = FS cos0
i.e. W = FS …(ii)
i.e. W = product of the force and the distance through which the body moves in the direction of the force.
This type of work is said to be positive. Therefore, work done by a force is positive is q < 90o
Examples of Positive Work:
(1) When a spring is stretched, the work done by the stretching force is positive as the force acts in the direction of displacement of the spring.
(2) When a body falls freely under gravity, the work done by gravity is positive as force (gravity) and displacement of the body are in the same direction.
(3) When a gas taken in a cylinder expands, work done by the force is positive as the displacement is in the direction of the force.
Case II:. When the force acting on a body and its displacement are in the opposite direction
In this case, q = 180o. Therefore, from eqn (i), we have
W = FS cos180 = FS(-1)
Or W = -FS …. (iii). This type of work is said to be negative. Therefore, work done by a force is negative if q > 90o.
Examples of Negative Work:
(i) The work done against friction is negative as the frictional force is always in direction opposite to displacement.
(ii) Work done in lifting a body is negative as gravitational force and displacement are in the opposite direction.
Case III:. When force and displacement are at right angle to each other.
In This case q = 90o
From eqn (i), we have
W = FS cos90 = FS . 0 = 0
Therefore, no work is done by a force which acts at right angle to the direction of displacement of the body.
Examples of Zero Work:
(i) The work done by the centripetal force acting on a body moving in a circle with uniform speed is zero as it is always at right angle to the direction of motion of the body.
W = FS cos90
= FS (0)
= 0
(ii) A person carrying a load on his hand and walking on a horizontal road does no work as the force is acting at right angle to displacement.
Case IV: If S = 0, then from eqn. (i), we have
W = f x 0 x cosθ = 0
Therefore, no work is done by because if it can not displace a body on which it acts.
Work: In physics work is said to be done when a force acting on a body displaces it through a certain distance. The work by a constant force is measured by the dot product of force will displacement.
i.e. W = F.S or W = F S cosθ …(1)
where F = force and S = displacement
And θ = angle between F and S.
From eq.(1), we have W=F cosθ S. Therefore, work done by a force is equal to the product of the component of the force in the direction of displacement of the body and the distance through which the body moves.
As work is the dot or scalar product of two vectors (force and displacement), therefore, it is a scalar quantity.
Special cases:
CaseI: When the body moves in the direction of the force. In this case, q = 0o.
from eq (i), we have
W = FS cos0
i.e. W = FS …(ii)
i.e. W = product of the force and the distance through which the body moves in the direction of the force.
This type of work is said to be positive. Therefore, work done by a force is positive is q < 90o
Examples of Positive Work:
(1) When a spring is stretched, the work done by the stretching force is positive as the force acts in the direction of displacement of the spring.
(2) When a body falls freely under gravity, the work done by gravity is positive as force (gravity) and displacement of the body are in the same direction.
(3) When a gas taken in a cylinder expands, work done by the force is positive as the displacement is in the direction of the force.
Case II:. When the force acting on a body and its displacement are in the opposite direction
In this case, q = 180o. Therefore, from eqn (i), we have
W = FS cos180 = FS(-1)
Or W = -FS …. (iii). This type of work is said to be negative. Therefore, work done by a force is negative if q > 90o.
Examples of Negative Work:
(i) The work done against friction is negative as the frictional force is always in direction opposite to displacement.
(ii) Work done in lifting a body is negative as gravitational force and displacement are in the opposite direction.
Case III:. When force and displacement are at right angle to each other.
In This case q = 90o
From eqn (i), we have
W = FS cos90 = FS . 0 = 0
Therefore, no work is done by a force which acts at right angle to the direction of displacement of the body.
Examples of Zero Work:
(i) The work done by the centripetal force acting on a body moving in a circle with uniform speed is zero as it is always at right angle to the direction of motion of the body.
W = FS cos90
= FS (0)
= 0
(ii) A person carrying a load on his hand and walking on a horizontal road does no work as the force is acting at right angle to displacement.
Case IV: If S = 0, then from eqn. (i), we have
W = f x 0 x cosθ = 0
Therefore, no work is done by because if it can not displace a body on which it acts.
