Work Done By A Force

  • Work done by a force refers to the amount of energy transferred. It is a scalar quantity by dot product with a SI unit of JouleJ=kg⋅m2⋅s−2

  • Work done in calculus formed is expressed as below.

  • Work-energy theorem states that change in kinetic energy is equal to work done on an object. 

Basic Exercise Problems

 (a) How much work is done by a horizontal force of 150N that acts on a crate for a distance of 10m?
(b)How much work is done on the crate across the frictionless surface?
(c) How much work is done on the crate if the crate returns to rest due to friction.

 

A 40kg box is pulled 100m by a tension force of 200N at 30 degrees above the horizontal to the right. A constant kinetic frictional force of 80N impedes the motion of the box.

  • (a) What is the work done by the tension force?
  • (b) How much work is done by friction?
  • (c) Calculate the net work done on the box.

Energy

  • Energy, in physics, the capacity for doing work. It may exist in potential, kinetic, thermal, electrical, chemical, nuclear, or various other forms.
  • Energy has a SI unit of Joule, represented by the letter of J, and has a base unit of kg⋅m2⋅s−2.
  • Same with work, energy is also a scalar quantity. 

In this section, we will be mainly talking about kinetic energy, spring potential energy, and gravitational potential energy

https://www.miningreview.com/energy/changing-the-landscape-of-centralised-power-supply-2/

Kinetic Energy

  • Imagine a scenario where you throw a ball into the air as hard as you can. The ball in motion moves in the air at a high speed, then you know that the ball must possess some sort energies, which is known as the kinetic energy. 

Kinetic energy

  • Kinetic energy is the energy that an object has because of its motion.
  • K= (1/2)mv^2, where m is the mass of the object, and v is the velocity.
  • Kinetic energy is a scalar quantity with a SI unit of Joule J= kg⋅m2⋅s−2
  • Work-energy theorem: change in kinetic energy is equal to work done on an object

Spring Potential Energy 

  • Spring energy is a form of potential energy that is also known as elastic potential energy. The formula we used to calculate spring potential energy is listed below:

Challenging Questions

Extension: Spring, Circular Motion, and Simple Harmonic Motion

  1. A vertical spring is at rest and starts to move after you stretched the spring. What is the spring's maximum stretch. Express your answer in term of spring constant K, mass m, gravitational g, and change in position x.

  2. Same condition as above. when is the spring's speed fastest?

  3. How could you explain the motion of a spring in term of circular motion if you have learnt it.

  4. Sketch the diagram of work done by a spring if a constant force is applied.

  5. Now, how could you prove the formula for spring potential energy by using your knowledge of work done. (Integration)

Gravitational Potential Energy (Work Done by Gravity)

  • Gravitational potential energy is the energy stored in an object due to its position above the earth's surface area. This is due to the force of gravity acting on an object. Gravitational potential energy is calculate by the formula of Ep = m × g × h
    • Ep(Joule)= gravitational potential energy
    • m (kg) = mass
    • g (N/kg) = gravitational acceleration

https://www.pathwayz.org/Tree/Plain/GRAVITATIONAL+POTENTIAL+ENERGY

Recap