# Work energy principle and power

• MHB
• Shah 72
In summary, the problem involves two particles, X and Y, attached to a string of length 4.8m passing over a fixed smooth pulley. Particle X of mass 2kg is held at ground level, 3m below the pulley, while particle Y of mass mkg hangs vertically on the other side. The tension in the string, denoted by T, can be expressed as T=40m/(m+2) N while both particles are moving. To find how close particle X gets to the pulley in subsequent motion, the work energy principle can be used, with work done on the 2kg mass by the force of tension given by W=(T Newtons) x (1.2 meters
Shah 72
MHB
Particle X of mass 2 kg , and particle Y of mass m kg are attached to the ends of a light inextensible string of length 4.8m. The string passes over a fixed smooth pulley and hangs vertically either side of the pulley. Particle X is held at ground level, 3m below the pulley. Particle X is released and rises while particle Y descends to the ground

a) Find an expression in terms of m for the tension in the string while both particles are moving.
By getting two equations
T-20=2a and T-10m=-ma
Solving simultaneously and removing a I got mT+2T-40m=0,
I finally got T=40m/(m+2) N
b) use work energy principle to find how close particle X gets to the pulley in subsequent motion.
Iam not able to get this ans. Pls help

work done on the 2kg mass by the force of tension ...

$W = (T \, Newtons) \cdot (1.2 \, meters) = 2gH$, where $H$ is the highest point mass X rises above ground level.

skeeter said:
work done on the 2kg mass by the force of tension ...

$W = (T \, Newtons) \cdot (1.2 \, meters) = 2gH$, where $H$ is the highest point mass X rises above ground level.
Thanks!

The problem I have with
"a) Find an expression in terms of m for the tension in the string while both particles are moving.
By getting two equations
T-20=2a and T-10m=-ma"
is that you have not said what either "T" nor "a" are!

I can guess that "T" is the tension in the string and that "a" is the acceleration of the particles but you really should have said thar.

## 1. What is the work energy principle?

The work energy principle states that the work done on an object is equal to the change in its kinetic energy. In other words, the net work done on an object will result in a change in its speed or direction of motion.

## 2. How is work calculated using the work energy principle?

Work is calculated by multiplying the force applied on an object by the distance over which the force is applied. This can be represented by the equation W = Fd, where W is work, F is force, and d is distance.

## 3. What is the relationship between work and energy?

Work and energy are closely related concepts. Work is the transfer of energy from one object to another, and energy is the ability to do work. The work energy principle shows that the work done on an object will result in a change in its energy.

## 4. How does power relate to the work energy principle?

Power is the rate at which work is done or energy is transferred. It is calculated by dividing the work done by the time it takes to do the work. The work energy principle can also be used to calculate power by dividing the change in energy by the time it takes for the change to occur.

## 5. How is the work energy principle applied in real life?

The work energy principle is applied in many real-life situations, such as when a person lifts a heavy object or when a car accelerates. It is also used in the design and operation of machines, such as engines and turbines, to understand and optimize their performance.

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