Work Energy And Power

Mechanical work is the force applied through a distance, defined mathematically as the line integral of a scalar product of force and displacement vectors

Given
hence

In an inelastic collision, kinetic energy is not conserved but the total energy and momentum remains conserved.
Momentum before collision = Momentum after collision



Kinetic energy before collision


Kinetic energy after collision


Loss in kinetic energy

The variation of potential energy with distance is
Hence, parabolic graph is obtained.

The ratio of masses
Therefore,
Applying law of conservation of momentum



Therefore, velocity of lighter mass is opposite to that of heavier mass.

Given, force
or
or
or
or

In a collision, the effect of external forces such as gravity or friction are not taken into account as due to small duration of collision (At) average impulsive force responsible for collision is much larger than external force acting on the system and since this impulsive force is 'internal' therefore the total momentum of system always remains conserved. In a collision total energy is also conserved. In an inelastic collision kinetic energy appears in other forms. In some cases

such as when initial KE is converted into internal energy of the product while in other cases

such as when internal energy stored in the colliding particles is released.

Given,
and
Work done

If two bodies stick together after collision and move as a single body, the collision is said to be inelastic.

Given, and
Scalar product
Using
we have

As there is no air resistance and gravitational force is a conservative force, we can apply mechanical energy conservation.

Work done by lift = change in PE of weight

So power of crane

change

As the road does not move at all, therefore, work done by the cycle on the road must be zero.

units

According to law of conservation of linear momentum,

Step 1: Define potential energy.
Potential energy is the energy stored in a system due to the position or configuration of an object relative to a reference point, such as the force exerted by gravitational or electromagnetic fields.

Step 2: Gravitational or electromagnetic fields.
Gravitational potential energy is given by , where is mass, is gravitational acceleration, and is height.
This type of energy depends on the force exerted by these fields.

Step 1: Understand the formula for work done.
The work done in lifting the book is given by: where is the force exerted (which is the weight of the book), and is the displacement (which is the height of the bookshelf).

Step 2: Work done depends on the weight of the book and the height.
The weight of the book , where is the mass and is the acceleration due to gravity.
Therefore, the work depends on the weight and height.
Time does not affect the work done, only the power.

Step 1: Recall the formula for energy.
Energy is given by the formula:
Step 2: Effect of doubling force and length.
If both force and length are doubled, the energy will change as follows: So, the new energy will be 4 times the original energy.