# Can Work be Negative? [Explained with daily life examples]

Work is a form of energy that is considered a scalar quantity. It depends on the force on an object and the displacement traveled by the object. But is work also have a negative sign?

The work can be negative, positive, or zero. The sign of the work depends on the relation between the direction of the force and displacement. The work is negative when the component of the force which is parallel to the displacement vector is in opposite direction to the displacement.

The sign convention of work in thermodynamics and chemistry depends on another factor i.e. work by the system or work on the system.

To know about the different considerations for the negative work in physics, thermodynamics, and chemistry, keep reading below.

Contents:

## Can work be negative in physics?

Work by the force acting on an object can be negative, positive, or zero. It depends on the direction of the individual force acting on the object and the direction of displacement.

If the component of the force (F.cosθ) parallel to the displacement vector (S) is in the same direction as displacement (see below left figure), then the force does positive work.

If the component of the force parallel to the displacement vector is in the opposite direction of displacement (see below right figure), then the work done by the force is considered negative.

The equation for the work done by the force is given by,

W = F.S.cosθ

Where,
F = Force
S = Displacement
θ = Angle made by force and displacement vectors

The value of cosθ is positive for 0°<θ<90° and becomes negative for 90°<θ<180°. Thus the sign of the work is given by,

Work is positive when [0°<θ<90°]
Work is zero when [θ = 90°]
Work is negative when [90°<θ<180°]

The below figure summarizes the sign convention of the work by force based on the angle between displacement and force vectors.

Here the force F1 and F2 do positive work and their horizontal component is in the same direction as the displacement.

The force F4 and F5 does negative work as their horizontal component is in opposite direction as the displacement. And Force F3 and F6 do zero work as these forces are perpendicular to the displacement vector.

Work is also equal to the change in the Kinetic energy of the object. Thus if the force lowers the KE of the object, then the work by the force is negative.

## Negative work examples:

1] Word done by gravitational force while Lifting an object:

In the above figure, the person is lifting a container from the ground. Here the two forces acting on the container: the lift force applied by the person and the gravitational force (weight of the container).

Here the container is lifted in an upward direction thus the displacement is in an upward direction.

As the lift force is in the same direction as the displacement, thus the force applied by the man is doing positive work on the container.

The gravitational force acts in the opposite direction of the displacement, thus the gravitational force does negative work on the container.

Let me explain this in more detail with the help of another example.

2] Work by frictional forces:

Consider a person pushing a Box on the ground. As shown below, the box is subjected to different forces.

Let’s discuss the negative and positive work done by forces on the system.

Negative Work:

If the component of the force is in the opposite direction of the displacement, then this force does negative work.

In the above figure, the frictional force (FR) is acting in the opposite direction of the displacement of the box. It is opposing the motion of the box and tries to lower the K.E. of the box.

Thus the frictional force in the above example is doing negative work.

Positive work:

The work done by a force will be positive if that force (or its component) is able to generate a displacement in the same direction.

It means that, if one of the components of the force is in the same direction as the displacement, then this force does positive work.

In the above figure, the force (F) is acting in the direction of the displacement vector. Thus the work done by force F is positive.

Zero Work:

The box weight (mg) and normal reaction (N) are perpendicular (90°) to the displacement direction.

∴ W = F.S.cosθ = F.S.cos(90°) = 0

Thus the box weight (mg) and normal reaction (N) do zero work on the box.

## Significance of negative work in Physics:

Here are some examples to understand the significance of negative work:-

a] Work by braking forces: The braking force acts in the opposite direction of the displacement of the vehicle. These forces lower the kinetic energy of the vehicle to stop the vehicle.

Thus the work done by the braking forces is negative.

b] Work by frictional forces:

Consider an example of a tire of the vehicle rolling over a road surface. The frictional force between the tire and the ground acts opposite to the direction of displacement of the tire.

This frictional force decelerates the wheels of the vehicle and decreases the KE of the vehicle. Thus these frictional forces do negative work to decelerate the vehicle.

## Can work be negative in thermodynamics?

In thermodynamics, the work done by the system is considered positive and work supplied to the system is considered negative.

The sign convention of work and heat in thermodynamics is as follows,

In a thermodynamic system, the main focus is on the work output from the system (e.g. Heat engines). Or it can be said that, the surrounding is considered a frame of reference.

Thus if the work is supplied by the surroundings to the system, then the work is considered negative, while if the work is supplied by the system to the surrounding, then the work is considered positive.

A heat engine runs to provide a work output for running the other equipment.

In the heat engine, the work is supplied by this surrounding for the compression of gases. Here as the work is supplied to the system for compression, which is considered as negative.

While after the combustion the high-pressure gases undergo expansion. Here it does work by forcing the piston outward to actuate the further system. This work output from the engine is considered positive.

## Can work be negative in chemistry?

In chemistry, the sign convention of work is different, this is because here the chemical system is considered a frame of reference.

Thus here any energy gained by the system is considered positive while energy loosed by the system is considered negative.

Thus the work added to the chemical system is considered positive and work done by the chemical system is considered negative.

The sign convention of work and heat in chemistry is as follows,

Let me explain with an example.

Consider a case of a high-pressure gas enclosed in a cylinder and a movable piston undergoing expansion. Here the gases lose energy in the form of work for pushing out the piston. Thus the work of expansion of gases is considered negative.

In opposite, the work supplied is considered positive (e.g. Work done by a stirrer to mix fluid).

## Final Words:

In the context of physics, Work by the force is negative if it opposes the motion of the object. While in other considerations (thermodynamics and chemistry), the sign of work depends on the direction of the flow of work between the system and the surrounding. Pratik is a Graduated Mechanical engineer. He enjoys sharing the engineering knowledge learned by him with people.