Introduction to Work Done
Sep 26, 2022, 16:45 IST
In our daily life, we observe various types of work, from waking up to pushing a cylinder on the grass. Have you ever noticed something in all the work you do every day? Also, is there anything we need to do to do any work? Well, the thing required is power. To define it, if we push a box a certain distance 'd' by applying a force 'F,' we do some work and multiply the force, and 'd' is the work done.
Therefore, for every work we do, we need a force, or work is done when a force moves something.
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Work done in Physics
When we apply a pull on the block with some force "F," the body moves with a specific acceleration, or its velocity increases or decreases depending on the direction of the force, as the velocity increases or decreases, the kinetic energy of the system changes. We know that energy can neither be created nor destroyed, so energy must be converted into another form. In this term, it is called work done. Energy decreases when negative energy is completed, and energy increases when positive work is completed. Now we will perceive how to determine the work done.
Work done Definition
Work done is developed so that it contains both the forces exerted on the body and total displacement.
This block is led by a constant force represented as "F." The purpose of this force is to move the body to a specific distance d in a straight path in the direction of the force.
Work Done for the Motion of a Block
Consider a block that is placed on a horizontal frictionless surface. A constant force F acts on this block. The main purpose of this force is to move the body a certain distance along a straight or linear path in the direction of the force.
So, the total work done by this force is equal to the product of the magnitude of applied force and distance traveled by the body. Work done formula is: W = F x d
In this case, the force acting on the block is constant, but the direction of the force and the direction of displacement determined by this force are different. Now the force F acts at an angle θ on (d) the displacement.
W = (|F| cosθ) |d|
As, we know that work done is known as the multiplication of magnitude of displacement d and the force component in the direction of displacement.
Derivation of Work done formula
As we k know that work done by force (F) is equal to the change in kinetic energy
W = 1/2mv2 - 1/2mu2 = 1/2m(v2-u2).....(1)
W = 1/2m(2as)
W = m x a x s
Now, from Newton's second law equation, F = ma (substituting now for F).
W =F x s
Since the K.E. is the work done by a force 'F,' so W = F x s
Work done by the system
When describing the work, we emphasize the effects that the system does not work on its surroundings.
Thus, we express work as positive when the system exerts any effort on the surroundings (i.e., energy leaves the system). If work is negative, then work is done on the system (i.e., energy added to the system).
Types of Work Done
- Positive Work - If a force displaces an object in its direction, the work is positive. An example of this type of work is the motion of a football falling toward the earth, where the ball's motion is in the direction of the gravitational force.
- Negative Work - When both the force and displacement are in opposite directions, the work is said to be negative. For example, when a football is thrown upwards, the displacement will be upward; however, the force due to the earth's gravity will be downward.
- Zero Work - If the direction of displacement and force are perpendicular to each other, then the total work done on the oject by the force is zero. For example, when we push hard on a wall, the force we exert on the wall does not work because the wall displacement is d = 0.
Relation between Work Done and Energy
Both the work and energy are directly proportional to each other. Work done by an object can be represented as:
W = 1/2 mvf2 - 1/2 mvi2
Where,
m = mass of the object
W = work done by an object
vf = final velocity of an object
vi = initial velocity of an object
Work-energy principle states that:
The work done by all the forces acting on a particle or the Work of the resultant force F(resultant) is equivalent to the change in kinetic energy of a particle.
Solved Example
Q1. Calculate the work done if 10 N of force acts on the body showing the displacement of 2 m.
Ans. Given,
F (Force) = 10 N,
s (Displacement) = 2 m,
W (Work done) = F × s
= 10 N × 2 ma
= 20 Nm.
Q2. Find the work done for 2-newton force and 3-meter displacement, and the angle between force and displacement is 45 degrees.
Ans. Given,
Force F = 2 N,
Displacement d = 3 m,
θ = 45o
Work done,
W = Fd cos θ
W = 2N × 3m cos 45o
W = 3.51 Nm.
Frequently Asked Question (FAQs)
Q1. What factors affect work done?
Ans. An amount of work done when a force acts on a body depends on the size of the force acting on the object. The force's distance causes the body to move in the direction of the force.
Q2. Is work done dependent on time?
Ans. Work is a time-based quantity; it usually depends on how fast a force displaces an object.
Q3. Is work done equal to energy?
Ans. The total rate of doing work is equal to the total rate of using energy. Since the force transfers one unit of energy when it does one unit of work.
Q4. What can work be converted to?
Ans. Work can be completely converted into heat. Joule did such an experiment when he measured the mechanical equivalent of heat. Thus, heat cannot be completely converted into work. Heat carries entropy, and work carries none.
Q5. In which process the work done is zero?
Ans. An isochoric process is one in which the volume is held constant (V=constant), meaning that the total work done by the system will be zero.
