Work can be negative if the applied force is in the opposite direction to the moving object’s displacement. To know the difference between positive and negative work, we need to understand the relationship between work applied force and work done.
This article answers the question “Can work be negative?” along with the definition of work, and units of work.
Table of Contents
Definition of work
Work (W) is the product of force (F) and displacement (d) in the direction of the force.
It is a scalar quantity, and its unit is the joule.
W = F x d
Units
- Joules (MKS system).
- N.m
- kg*m2/sec2.
Can Work Be Negative?
Work is done when a force acting on a body displaces it in the direction of a force. For instance, the work done by a moving object equals 1 Joule when a force of 1 Newton is applied over 1 meter of distance. Since the applied force can be negative or positive, work can be negative or positive.
The motion of a body against the force of friction is an example of negative work.
Here are a few examples of negative work in physics:
- Climbing a ladder: When you climb a ladder, you employ an upward force to fight the downward force of gravity. Because it opposes the direction of gravity, this force does negative work.
- Pumping water uphill: When you use a pump to transport water uphill, you are working against gravity, which is pulling the water down. This is negative work because the force you apply opposes the direction of gravity’s force.
- Lifting an object against friction: When you lift an object off the ground and drag it across a rough surface, you apply an upward force to overcome friction. Because it opposes the direction, this force causes negative work.
- Slowing down a moving thing: When you use a force to slow down a moving object, you are doing negative work since the force you are applying is in the opposite direction of motion. When you apply the brakes to a moving car, for example, the force you exert slows the car down, which is negative work.
- Swimming against a current: If you are swimming in a river and the current is flowing in the opposite direction than you wish to travel, the force you use to swim is negative effort since it is against the direction of the current.
These are just a few examples of negative physics work. Understanding negative work is essential in many aspects of physics, including mechanics, thermodynamics, and energy conservation.
What is the unit of work?
Unit of work is the joule. One joule is the amount of work done when a force of 1 Newton is applied over a distance of 1 meter.
Joule = N.m
Joule= kg.m2/sec2
Key Points
| Definition of work | Work is the product of force and displacement. Work done is directly proportional to the applied force and distance covered. |
| Unit of work | Joule = N.m (kg.m2/sec2). |
| Scalar quantity | Work is a scalar quantity. It can be completely described by magnitude alone. |
| Can work be negative? | Yes, work is negative if the displacement is in the opposite direction of the applied force. |
| Daily life examples of work | Walking upstairs, Lifting a book, and pushing something. |
Work done by an inclined force
Consider a force (F) applied to an object. The force F is making an angle θ with the surface on which the body is moved, as shown in the figure at left. The applied force F can be resolved into its perpendicular components Fx and Fy.
Fx = Fcosθ ——— (1)
Fy = Fsinθ ——— (2)
When force and displacement are not parallel, then only the x-component of force (Fx) causes the body to move on the surface.
W = F x d since Fx = Fcosθ
W = Fcosθ d = Fdcosθ
Examples
- The work (W) done in lifting a brick of mass 2 kg to a height of 5m above ground will be 100J.
- Suppose a man pulls a cart through 35 m with a force of 300 N. The W will be 10500 J.
- When a person takes a bucket to some distance, his work done is zero because force and displacement are perpendiculars.
- If we lift a load from the earth to some height, the work is done.
Factors On Which Work Depends
- Force acting on the body (F)
- Displacement of the body (d)
- The angle between force and displacement (θ)
Dimensions of Work
F =ma, Therefore, 1N = 1kg x 1m/sec2
[F]=[MLT-2]
W =F x d
[W]=[MLT-2][L] = ML2T-2
Different Cases Of Work Done
Work done depends upon the angle of the applied force. The table below shows different cases of work being done with different force angles.
| Angle (θ) | W = Fdcosθ | Explanation |
| 0 | W = Fdcos(0)= Fd | The work done will be maximum when the angle between force and displacement will be zero |
| 90 | W = Fdcos(90)= 0 | The work done will be zero when force and displacement are mutually perpendicular to each other. If a person takes a bucket to some distance, W is zero because the force and displacement are perpendicular to each other |
| 180 | W = Fdcos(180)= -Fd | The work done will be negative when force and displacement are opposite to each other. When a body moves against the force of friction or against the force of gravity. |
The Definition of Work in Simple Words
- Work is done when a force acting on a body displaces it in the direction of a force.
Graphical Representation of Work Done By A Constant Force
The area under a force-displacement curve represents the work done by a constant force.
Consider a constant force F applied to an object that displaces it by the distance d along the x-axis. The force is constant along the y-axis.
When constant force F and displacement d are in the same direction.
W = Fdcosθ (F and d are in the same direction, so θ is zero)
W = Fd
On the graph, the green shaded area in the figure is OPQR which is also Fd. Hence, the area under the force-displacement curve measures the work done.
Example problems
# 1: Ten bricks, each 6 cm thick and weighing 1.5 kg, lie flat on a table. Find W if we need to stack all the bricks.
Mass = 1.5 kg
Height of each brick = h = 6cm = 0.06m
No of bricks = 10
W = 0+mgh +mg(2h) + mg(3h) +…mg(9h) = mgh(45) = 45mgh
W = 45 x 1.5 x 9.8 x 0.06 = 39.69 J = 40 Joule
# 2: A raindrop falls vertically at a constant speed under the influence of the forces of gravity and friction. In falling through 100m, find W in terms of gravity and friction.
mass = 3.35 x 10-5 kg; height = 100 m.
Work done by gravity = Wg = W.h = Whcosθ = Whcos(0)
Wg = Wh =mgh =3.35 x 10-5 x 9.8 x 100 = 0.0328J
Work done by friction = Wf =fhcosθ = fhcos(180)
Wf = fh(-1) = -fh = wh =-mgh
Wf =-3.35 x 10-5 x 9.8 x 100 =-0.0328J
Summary
- The answer to the question “Can work be negative?” is yes.
- The work is negative if the applied force is in the opposite direction to the displacement of the moving object.
- Work is a scalar quantity and its unit is the joule.
- One joule is one unit of work. Work is one joule if a force of 1 Newton is applied across a distance of 1 meter.
- When the angle between force and displacement is zero, the work done is maximal.
- If force and displacement are in opposition to each other, the work done is negative.
- When force and displacement are perpendicular to each other, the work done is zero.
More Topics
Relativistic Kinetic Energy
Power Units- The Basics
Can Momentum be Negative?
Velocity Time Graph
Can Displacement be Negative?
Frequently Asked Questions
Some of the frequently asked questions are given below
1. Can force be negative?
To answer the question “can force be negative”, we need to understand the concept of positive direction and negative direction.
- force is negative. If the applied force is in the opposite direction to the displacement of the moving object.
- Forces that are aimed at the right are usually called positive forces.
- Forces that are aimed to the left are usually said to be in a negative direction.
2. What is instantaneous velocity?
The velocity of an object at any single instant or point is called instantaneous velocity.
It is similar to average velocity, except the time interval is infinitely small.
The formula for instantaneous velocity is the limit as the time approaches zero of the change in displacement over the change in time.
3. What is the momentum equation?
The momentum equation is simply the product of the mass and velocity of a moving object.
If an object is moving and has mass, then it has momentum.
The momentum of a body refers to the quantity of motion a body possesses due to its mass and velocity.
4. What is the kinetic energy formula?
A moving object’s kinetic energy equals half of the product of its mass and its velocity squared.
Because an object’s mass can never be zero and the square of velocity is positive, kinetic energy is always positive.
5. What is energy definition science?
In physics, energy is the ability to perform work. It can take many forms, including potential, kinetic, thermal, electrical, chemical, radioactive, and others. Furthermore, there is heat and work—that is, energy in the transmission of energy from one body to another.
6. What is the work-energy equation?
According to the work-energy theorem, the net work done on an item by forces equals the change in its kinetic energy.
7. What is the potential energy formula?
For the gravitational force, the formula of potential energy equals mgh, where m is the mass in kilograms, g is the gravity acceleration (9.8 m/sec2 at the earth’s surface), and h is the height in meters.
8. What is strain energy?
Strain energy is a form of potential energy that is stored within materials that have been subjected to strain deformation. When an item is deformed from its unstressed state, the external work done on it is transformed into (and is considered equivalent to) the strain energy contained in it. It is measured in N-m or Joules.
9. Can displacement be negative?
Displacement can be negative since it is a vector variable that depends on magnitude and direction. The negative sign just indicates the direction. Check the full article here” can displacement be negative?”.
10. What is a state function?
A state function is a property that depends on the state of a system and is independent of the path taken to get it. Pressure and temperature, for example, are state functions.
11. Can momentum be negative?
Momentum is a vector quantity that is calculated by multiplying the mass of an item by its velocity. If the item’s velocity is negative, i.e., the object is traveling in the negative direction, the momentum will be negative as well. Check the full article here” can momentum be negative?”.
12. What is gravitational potential energy?
Gravitational potential energy (w) is the energy that an item has as a result of its location in a gravitational field. If the item is pushed straight up at a constant speed, the force (F) necessary to hoist it to the height (h) is equal to its weight (mg).
13. Relativistic kinetic energy?
According to the relativistic kinetic energy equation, when an object’s velocity approaches the speed of light, its energy approaches infinity. As a result, exceeding this speed restriction is impossible.
14. Gamma decay?
Gamma decay is the discharge of a gamma (γ) ray photon, a type of high-energy electromagnetic radiation, as a result of the radioactive decay of a nucleus. The energy spectrum is often in the 100 keV to 10 MeV range.
W = mgh = 10 x 9.8 x 10 = 980J = 0.98kJ
mass = 1kg
height =1meter
W = mgh =1 x 9.8 x 1 = 9.8 J (Positive value)
Author
Umair Javed
Umair has been working at Whatsinsight since 2020 as a content writer.
He has a Masters’s degree in Materials Science.
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