How to Calculate Work Done: Step-by-Step Examples
We observe various types of work in our day-to-day life starting from waking up to pushing a lawn roller, and so on. Do you notice something in all the work that you do daily? Also, is there anything that we need to do for doing any work? Well, the thing required is force. To define, if we push a box by some distance ‘d’ by applying force ‘F’, we do some work and the multiplication of Force and ‘d’ is the work done.
Therefore, for every work we do, we need force or the work is done when a force moves something.
Work Done in Physics
When we give a thrust to a block with some force ‘F’, the body travels with some acceleration or, also, its speed rises or falls liable to the direction of the force. As the speed surges or declines, the kinetic energy of the system alters. We know energy can neither be formed nor be demolished, so the energy must be converted into some other form. In this stance, it is termed as work done. The energy decreases when negative energy is completed, and the energy increases when positive work is completed. Now we will perceive how to determine work done.
Definition of the Work Done
Work done is elaborated in such a way that it includes both forces exerted on the body and the total displacement of the body.
This block is preceded by a constant force F. The purpose of this force is to move the body a certain distance d in a straight path in the direction of the force.
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Now, let us do the work done derivation.
What is Work Done for the Motion of a Block?
Consider a block located on a frictionless horizontal surface. A constant force F is acted upon this block. The purpose of this force is to move the body through a certain distance in a straight path in the direction of the force.
Now, the total work done by this force is equal to the product of the magnitude of applied force and the distance traveled by the body. Scientifically Work done formula will be given as,
W = F * d
In this case, the force exerting on the block is constant, but the direction of force and direction of displacement influenced by this force is different. Here, force F reacts at an angle θ to the displacement d.
W = (|F| cosθ) |d|
We know that work done is defined as the multiplication of magnitude of displacement d and the component of the force that is in the direction of displacement.
Derivation for the Work Done Formula
We know that the Work done by force (F) is equal to the change in kinetic energy.
\[W=\frac{1}{2mv^{2}}-\frac{1}{2mu^{2}}=\frac{1}{2m}(v^{2}-u^{2})\] ……..(1)
We know that according to third equation of motion: v2 - u2= 2as …..(2)
Substituting equation (2) in (1) we get:
\[W=\frac{1}{2}m(2as)\]
\[W=m\times a \times s\]
We know from Newton's second law equation, F = ma (substituting now for F).
\[W=F.s\]
Since K.E. is the work done by a force ‘F’, so W = F.s
Work done by the system
While describing work, we emphasize on the effects that the system does not work on its surroundings.
Thus, we express work as being positive when the system makes any effort on the surroundings (i.e., energy leaves the system). The work is negative if work is done on the system (i.e., energy added to the system).
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Types of Work Done
Positive Work: If a force relocates the object in its direction, then the work done is positive. The example of this type of work done is the motion of the ball dropping towards the ground where the displacement of the ball is in the direction of the force of gravity.
Negative Work: When force & displacement are in reverse directions, then the work is assumed to be negative.
For instance, when a ball is thrown upwards, the displacement will be in upwards direction; however, the force because of the gravity of the earth will be in the downward direction.
Zero Work: If the direction of the force and the displacement are perpendicular to each other, the total work done by the force on the object is null.
For example, when we thrust hard against a wall, the force we are applying on the wall does not work, because in this case, the displacement of the wall is d = 0.
Work Done and Energy Relation
To move an object, it should be transferred to energy. Transferring energy can be in the method of force. This quantity of energy transferred by the force to move an object is termed as work done. Therefore, the relation between Work and Energy is related directly.
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We concluded that the work and the energy are directly proportional to each other. Work done by an object can be scientifically expressed as:
W = \[\frac{1}{2}\]mvf2 - \[\frac{1}{2}\]mui2
Where,
m = the mass of the object measured using kilograms.
W = the work done by an object measured using Joules.
vf = the final velocity of an object measured using m/s.
vi = the initial velocity of an object measured using m/s.
Therefore, the work-energy principle states that:
The total work done by all the forces acting on a particle or the work of the resultant force F(in subscript resultant) is equivalent to the change in kinetic energy of a particle.
FAQs on Work Done in Physics: Explained for Students
1. What is the scientific definition of 'work done' in Physics?
In Physics, work is defined as the transfer of energy that occurs when a force applied to an object causes it to move over a certain distance. For work to be done, two conditions must be met: a force must be exerted on the object, and the object must have a displacement in the direction of a component of that force.
2. What is the formula to calculate work done, and what does each variable represent?
The formula to calculate the work done by a constant force is: W = Fd cos(θ). In this equation:
- W is the work done, measured in Joules (J).
- F is the magnitude of the constant force applied, measured in Newtons (N).
- d is the magnitude of the displacement of the object, measured in metres (m).
- θ (theta) is the angle between the force vector and the displacement vector.
3. What are the different types of work done based on the angle between force and displacement?
There are three types of work done, determined by the angle (θ) between the applied force and the object's displacement:
- Positive Work: Work done is positive when the force (or a component of it) is in the same direction as the displacement (0° ≤ θ < 90°). This results in an increase in the object's energy.
- Negative Work: Work done is negative when the force (or a component of it) opposes the direction of displacement (90° < θ ≤ 180°). This typically removes energy from the object, like the work done by friction.
- Zero Work: Work done is zero when the force is perpendicular to the displacement (θ = 90°), or if there is no displacement at all (d=0).
4. Can you provide real-world examples of positive, negative, and zero work?
Certainly. Here are examples for each type of work:
- Example of Positive Work: Pushing a lawnmower forward. The force you apply is in the same direction as the mower's movement.
- Example of Negative Work: The force of friction acting on a sliding hockey puck. The puck moves forward, but friction acts in the opposite direction, slowing it down.
- Example of Zero Work: A waiter carrying a tray of food horizontally at a constant velocity. The force he applies is upwards (to counteract gravity), but the displacement is horizontal, making the angle 90 degrees.
5. What is the SI unit and dimensional formula for work?
The SI unit of work is the Joule (J). One Joule is defined as the work done when a force of one Newton displaces an object by one metre in the direction of the force. The dimensional formula for work is [ML²T⁻²], which is the same as the dimensional formula for energy.
6. How does the scientific meaning of 'work' differ from its everyday use?
In everyday language, 'work' refers to any physical or mental effort. For example, studying for an exam or holding a heavy suitcase is considered 'work'. However, in Physics, work requires displacement. If you hold a heavy suitcase without moving it, you exert a force but the displacement is zero, so no scientific work is done on the suitcase. The key difference is the mandatory requirement of motion caused by a force.
7. Under what specific conditions is the work done on an object zero, even if a force is applied?
The work done on an object is zero under three specific conditions, even if forces are present:
- When there is no displacement (d = 0). For instance, pushing against a solid wall that does not move.
- When the applied force and the displacement are perpendicular to each other (θ = 90°). For example, the gravitational force does zero work on a satellite in a perfectly circular orbit around the Earth.
- When the net force on the object is zero, though this is a less common interpretation as we usually calculate work done by individual forces.
8. How does the Work-Energy Theorem connect work and kinetic energy?
The Work-Energy Theorem is a fundamental principle stating that the net work done on an object by all forces is equal to the change in its kinetic energy (ΔK.E.). The formula is expressed as W_net = K.E._final - K.E._initial. This theorem provides a direct link between the mechanical action (work) performed on an object and the resulting change in its state of motion (kinetic energy).
9. What is the main difference in calculating work done by a constant force versus a variable force?
The method of calculation is the main difference. For a constant force, work is simply the product of the force component and displacement (W = Fd cos θ). For a variable force, the force changes as the object moves. In this case, work cannot be calculated with a simple multiplication. Instead, it is determined by calculating the area under the force-displacement graph, which mathematically corresponds to the integral of the force over the displacement (W = ∫F·dx).
10. How are the concepts of work, energy, and power related in Physics?
These three concepts are fundamentally interconnected. Energy is the capacity to do work. Work is the process of transferring that energy from one object to another or converting it from one form to another. Power is the rate at which work is done or energy is transferred. In simple terms, if work is the action of moving a rock, energy is the strength you needed to do it, and power is how quickly you did it (P = W/t).
