Work done on body equals to change in its kinetic energy is known as
work energy principle
Understanding the Work-Energy Principle
This question asks for the name of the physical principle that relates the work done on an object to the change in its kinetic energy. Let's break down the concepts involved:
What is Work Done?
In physics, work done ($W$) on an object occurs when a force ($F$) is applied to it, causing a displacement ($d$) in the direction of the force. Mathematically, it's often calculated as:
$$ W = F \cdot d \cdot \cos(\theta) $$
where $\theta$ is the angle between the force and the displacement.
What is Kinetic Energy?
Kinetic energy ($KE$) is the energy an object possesses due to its motion. It depends on the object's mass ($m$) and its velocity ($v$). The formula for kinetic energy is:
$$ KE = \frac{1}{2}mv^2 $$
The Work-Energy Principle
The principle that directly connects these two concepts is the Work-Energy Principle. It states that the net work done on an object is equal to the change in its kinetic energy.
This can be expressed mathematically as:
$$ W_{net} = \Delta KE $$
Where $\Delta KE$ represents the change in kinetic energy:
$$ \Delta KE = KE_{final} - KE_{initial} $$
Or, using the formula for kinetic energy:
$$ W_{net} = \left(\frac{1}{2}mv_f^2\right) - \left(\frac{1}{2}mv_i^2\right) $$
Here, $v_f$ is the final velocity and $v_i$ is the initial velocity of the object.
Analyzing the Options
- work done principle: While related, this is not the specific term for the relationship between work and the change in kinetic energy.
- work energy principle: This accurately describes the principle that net work done equals the change in kinetic energy.
- work velocity principle: This is not a standard physics term for this concept.
- speed displacement principle: This term doesn't correctly represent the relationship described.
Therefore, the statement "Work done on body equals to change in its kinetic energy" is known as the work energy principle.
Important Questions from Conservation of Mechanical Energy
A ball is thrown up at a speed of 2m/s. If g = 10m/s 2, then find the maximum height the ball will reach?
A particle of mass 40 g is thrown vertically upwards with a speed of 10 ms -1 . Find the work done by the force of gravity during the time the particle goes up.
Find the work done by the force of gravity during the time a particle of mass 50 gm goes up on being thrown vertically upwards with a speed of 10 m/s.
A uniform chain of mass m and length l is placed on a smooth horizontal table such that \(\frac{1}{4}\)th of its length is hanging from the edge of the table. The chain slips down. Find the kinetic energy of the chain when half of its length is hanging from the edge of the table.
Which of the following equation is also a special case of the work-energy (WE) theorem? (where a is acceleration, u and v are the initial and final speeds and s the distance traversed.)
