1800-212-7858 (Toll Free)
9:00am - 8:00pm IST all days
8104911739
For Business Enquiry

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

For any content/service related issues please contact on this toll free number

022-62211530

Mon to Sat - 11 AM to 8 PM

Work, Energy And Power

Share this:

Work, Energy and Power PDF Notes, Important Questions and Synopsis

SYNOPSIS

 

  • Work done by a constant force is
    begin mathsize 12px style text W=Fscos end text straight ϕ straight F with rightwards arrow on top. straight s with rightwards arrow on top end style
  • Work done can be positive, negative or zero.

  • Work done by a variable force

    begin mathsize 12px style straight W equals integral from straight s subscript 1 to straight s subscript 2 of straight F left parenthesis straight s right parenthesis ds end style
  • Work–energy theorem: The work W done by the net force on a particle equals the change in the particle’s kinetic energy.begin mathsize 12px style table attributes columnalign left end attributes row cell text FS= end text fraction numerator text 1 end text over denominator text 2 end text end fraction text mv end text to the power of text 2 end text end exponent text-end text fraction numerator text 1 end text over denominator text 2 end text end fraction text mu end text to the power of text 2 end text end exponent end cell row cell text W=K end text subscript text f end text end subscript text -K end text subscript text i end text end subscript end cell end table end style

  • Gravitational potential energy does not depend on the choice of the reference surface for measuring height.

  • Gravitational potential energy:
    1. Energy possessed by a body changes with height with respect to the surface of the Earth.
    2. GPE = −WGravitational Force 
  • Elastic potential energy; When a spring is elongated (or compressed), work is done against restoring force of the spring. This resultant work done is stored in the spring in the form of elastic potential energy.

  • Equilibrium
    If the forces are conservative, then
     begin mathsize 12px style straight F =- dU over dr end style
    For equilibrium,
    begin mathsize 12px style straight F equals 0 semicolon minus dU over dr = 0 end style
    if begin mathsize 12px style fraction numerator straight d to the power of straight 2 straight U over denominator dr to the power of straight 2 end fraction > 0 end style,then it is stable equilibrium.
    if begin mathsize 12px style fraction numerator straight d to the power of straight 2 straight U over denominator dr to the power of straight 2 end fraction < 0 end style ,then it is unstable equilibrium.
    if begin mathsize 12px style fraction numerator straight d to the power of straight 2 straight U over denominator dr to the power of straight 2 end fraction = 0 end style, then it is neutral equilibrium.
  • Law of conservation of mechanical energy:
    Total mechanical energy of the system always remains constant in the absence of dissipative forces.

  • Total mechanical energy of the system equals the sum of potential energy and kinetic energy.

  • Conservation and Non-Conservation forces

    • A force is said to be of the conservative category if the work done by it in moving a particle from one point to another does not depend on the path taken but depends only on the initial and final positions.

    • Work done by a conservative force around a closed path is calculated to be zero. Gravitational force, electric force and spring force are some of the examples of this category.

    • If the work done by a force in moving a body from one point to another depends on the path followed, then the force is said to be of the non-conservative category.

    • Work done by a non-conservative force around a closed path is cannot be zero. For example, both frictional and viscous forces work in an irreversible manner, and hence, a definite part of energy is lost in overcoming these frictional forces. (Mechanical energy is converted to other energy forms such as heat, sound etc.). Therefore, these forces are of the non-conservative category.

  • A conservative force is the negative gradient of potential energy function.
    F (x) = −DU/Dx

  • Motion in a Vertical Circle
  • A particle of mass m attached to one end of a string and rotated in a vertical circle of radius r with centre O.
    The speed of the particle will decrease as the particle travels from the lowest point to the highest    point but increases in the reverse direction due to acceleration due to gravity.
    begin mathsize 12px style straight T equals straight m open parentheses gcosθ straight plus straight v squared over straight r close parentheses end style
    At the highest point, begin mathsize 12px style straight T equals straight m open parentheses straight v subscript straight u to the power of straight 2 over straight r minus straight g close parentheses end styleAt the lowest point, begin mathsize 12px style straight T equals straight m open parentheses straight v subscript straight L to the power of straight 2 over straight r plus straight g close parentheses end style

  • Body inside a hollow tube
    begin mathsize 12px style table attributes columnalign left end attributes row cell text at lowest point end text end cell row cell text N=mg+ end text fraction numerator text mv end text to the power of text 2 end text end exponent subscript text 1 end text end subscript over denominator text r end text end fraction end cell row cell text at highest point end text end cell row cell text N+mg= end text fraction numerator text mv end text to the power of text 2 end text end exponent subscript text 2 end text end subscript over denominator text r end text end fraction text ;N end text greater or equal than text 0 end text end cell end table end style

    Minimum velocity to complete the circle
    begin mathsize 12px style text v end text subscript 1 greater or equal than square root of text 5rg end text end root end style

  • Power is the rate at which work is done or energy is transformed.

  • The unit of power is watt. 1 watt = 1 joule/second. It is a scalar quantity. Dimensions of power =
    begin mathsize 12px style straight M to the power of straight 1 straight L to the power of straight 2 straight T to the power of -3 end style
  • Linear momentum of an isolated system is always conserved in a collision.

  • A collision in which the total kinetic energy of the system is conserved is called elastic.
    A collision in which the total kinetic energy of the system is not conserved is called inelastic.

  • When two bodies collide, stick together and have a common final velocity, the collision is completely inelastic.


Show more

NEET Tests & Papers Solutions

Physics syllabus

Purchase Our Experts Course Packages

Enroll now to crack NEET

Testimonials

Ask Experts for NEET

Queries asked on Sunday and after 7 pm from Monday to Saturday will be answered after 12 pm the next working day.

View More

Chat with us on WhatsApp