Question

I want important notes and equations in chapter 8 physics 1
Related topics:

work done by constant forces

chapter 9:
1. kinetic energy

2. gravitational potential energy

chapter 10:

1. elastic potential energy

2. power

Answer 1

Work done by a constant Force

We define work done as :

  

• Work done by 1N force in displacing the object 1m will be 1N-m.
• Unit of work is (N-m) or Joule (J).
• Work is scalar quantity. It has only magnitude, no direction.
• If displacement is in the direction of force, then work is taken as positive.
• If displacement is in the opposite direction of force, then work is taken as negative.

The term “work” is used in everyday life quite frequently and we understand that it’s an act of doing something. For example, you are working right now on your grasp of Physics by reading this article! But, Physics itself might not agree on this. The Work-energy theorem explains the reasons behind this Physics of no work!

Work is said to be done when an acting force displaces a particle. If there is no displacement, there is no work done. You might get tired if you keep standing for a long time, but according to Physics, you have done zero work.

Thus, work is a result of force and the resulting displacement. Now, we already know that all moving objects have kinetic energy. So, there must be a relation between Work and kinetic energy. This relation between the kinetic energy of an object and workdone is called “Work-Energy Theorem”. It is expressed as:

Here, W is the work done in joules (J) and ΔK is the change in kinetic energy of the object. To learn how the Work-Energy Theorem is derived, we must first learn the nature of work as a scalar quantity and how two or more vector quantities are multiplied.

Workdone Under a Constant Force

We have already learnt about the equations of motion earlier and know that,

Here, v is the final velocity of the object; u is the initial velocity of the object; a is the constant acceleration and s is the distance traversed by the object. We can also write this equation as,

We can substitute the values in the equation with the vector quantities, therefore:

If we multiply both sides with m/2, we get:

From Newton’s second law, we know that F=ma, hence:

Now, we already know that W= F.d and, K.E. = (mv²)/2,
So, the above equation may be rewritten as:

Hence, we have:

Therefore, we have proved the Work-Energy Theorem. The Work done on an object is equal to the change in its kinetic energy.