In physical science, work is defined as energy transferred from or to a body by exerting a force. Usually, work is represented as the vector product of displacement and force. When a force is applied in the direction of displacement, positive work is done. On the other hand, negative work is done when a force is exerted in the opposite direction of the resultant displacement.
For example, when a cricket bat is held high up over the ground and then released, the work done by the force of gravity on the bat as it lands is equal to the product of distance to the ground (or displacement) and the bat’s weight (or force on the object). If the force ‘F’ is steady and the angle between the displacement ‘s’ and the force is θ, then the total work done is calculated by the formula,
‘W’ is the work completed by force, ‘d’ is the displacement produced by force, and ‘θ’ is the angle between the resultant displacement and the applied force.
Even though displacement and force are vector quantities, work is strictly a scalar quantity. It has no direction. Work transmits energy from one point to another or one type to another.
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Symbol |
\(\begin{array}{l}W\end{array} \)
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General Formulae |
\(\begin{array}{l}W = F\cdot s\end{array} \)
\(\begin{array}{l}W = \tau \theta \end{array} \)
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Dimension |
\(\begin{array}{l}\mathbf{M}\mathbf{L}^{2}\mathbf{T}^{2}\end{array} \)
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The SI unit of work is the joule (J). It is defined as the work needed to apply a force of one newton through a one-meter displacement. It is named after the physicist James Prescott Joule.
Force
Force can be stated as a pull or push that causes any body with a mass to vary its velocity and acceleration. Force is a vector as it has both direction and magnitude. Regardless of the state of the body (static or dynamic), when the force applied to a body is zero, the work produced by force is zero.
Displacement
Displacement can be stated as the shortest length between the starting point and ending point of any moving body. When resultant displacement caused by force is zero, then the total work produced by that force on that body is zero. For example, if force is applied on a compact wall and still fails to move it, then no work has been done on the wall.
The Angle between the Force Vector and the Displacement Vector
The work produced by force on a body can be zero, positive or negative. It depends on the displacement’s direction of the body relative to the force. For a body travelling in the opposite direction to the force’s direction, such as frictional force acting on a body travelling in the forward direction, the work produced due to the frictional force is negative.
Correspondingly, when a body experiences zero force when displacement’s angle is perpendicular to the direction of the applied force. For example, if a person lifts a body on his head travelling at an angle of 90° relative to the gravitational force, then the work done by the gravitational force on the body is zero.
Important Work Questions with Answers
1) What is meant by work?
Work is defined as energy transferred from or to a body by exerting a force. Usually, work is represented as the vector product of displacement and force. When a force is applied in the direction of displacement, positive work is done. On the other hand, negative work is done when a force is exerted in the opposite direction of the resultant displacement.
2) Give a real-life example of work.
For example, when a cricket bat is held high up over the ground and then released, the work done by the force of gravity on the bat as it lands is equal to the product of distance to the ground (or displacement) and the bat’s weight (or force on the object).
3) What is the formula of work done by a force on a body?
If the force ‘F’ is steady and the angle between the displacement ‘s’ and the force is θ, then the total work done is calculated by the formula,
‘W’ is the work completed by force, ‘d’ is the displacement produced by force, and ‘θ’ is the angle between the resultant displacement and the applied force. Even though displacement and force are vector quantities, work is strictly a scalar quantity. It has no direction. Work transmits energy from one point to another or one type to another.
4) What is the dimensional formula of work?
5 What is the SI unit of work?
The SI unit of work is the joule (J). It is defined as the work needed to apply a force of one newton through a one-meter displacement. It is named after the physicist James Prescott Joule.
6) What is the relationship between force and work?
Force can be stated as a pull or push that causes any body with a mass to vary its velocity and acceleration. Force is a vector as it has both direction and magnitude. Regardless of the state of the body (static or dynamic), when the force applied to a body is zero, the work produced by force is zero.
7) What is the relationship between displacement and work?
Displacement can be stated as the shortest length between the starting point and ending point of any moving body. When resultant displacement caused by force is zero, then the total work produced by that force on that body is zero. For example, if force is applied on a compact wall and still fails to move it, then no work has been done on the wall.
8) What is the importance of the angle between the force vector and the displacement vector?
The work produced by force on a body can be zero, positive or negative. It depends on the displacement’s direction of the body relative to the force. For a body travelling in the opposite direction to the force’s direction, such as frictional force acting on a body travelling in the forward direction, the work produced due to the frictional force is negative.
Correspondingly, when a body experiences zero force when displacement’s angle is perpendicular to the direction of the applied force. For example, if a person lifts a body on his head travelling at an angle of 90° relative to the gravitational force, then the work done by the gravitational force on the body is zero.
9) What is the work-energy principle?
The work-energy principle describes that the kinetic energy of a rigid body increases if an equal quantity of positive work is done on the body by the applied force acting on it. On the other hand, a reduction in kinetic energy is caused by an equal quantity of negative work done by the applied force. Therefore, if the total work is positive, the kinetic energy of the body increases by the quantity of work. If the total work done is negative, then the body’s kinetic energy decreases by the quantity of work.
10) What is kinetic energy?
It is the energy acquired by the body when it is in motion.
11) What is potential energy?
It is the energy acquired by a body because of stress within itself, position relative to others, electric charge, etc.
Practice Questions
1) Is work a scalar or a vector quantity?
2) What is the difference between work and energy?
3) What is the difference between kinetic energy and potential energy?
4) If a person lifts a body on his head travelling at an angle of _____ relative to the gravitational force, then the work done by the gravitational force on the body is zero.
5) _______ transmits energy from one point to another or one type to another.
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