Force


What is Force?

Force is an external agent that helps to change the state of object from rest to motion or motion to rest.

Force

F = ma where F is force in newtons, m is mass in kilograms, and a is acceleration in m/s2

When one object exerts a force on another object it always experiences an equal opposing force in return from the object it exerted the force on. Or in other words when two objects interact, the forces they exert on one another are equal and opposite. These forces are referred to as the action and reaction forces.Force is an interaction between objects that causes them to change motion. So, when you opened your locker door, your hand applied a force to the door, causing it to change its motion. We measure force in newtons (N), the scientific unit for measuring weight. One newton is equal to about 0.22 pounds. So, a girl weighing only 100 lb would be equal to approximately 445 newtons, or her force due to gravity (Fg). 

Examples of forces

Weight

Weight is the force of gravity, which is the pull of the Earth on an object. To understand the force of gravity the concept of mass needs to be understood as well.

Weight

W = mg where W is weight, m is mass in kilograms and g is acceleration due to gravity in m/s2 (on Earth, acceleration due to gravity is approximately 9.8 m/s2)

The mass of an object is the amount of matter it contains. Thus mass is a measure of how much stuff is in an object. Mass is measured in kilograms (kg) and is the same no matter where the object is located in the universe. For example and object of mass 10kg on the Earth will have the same mass of 10kg on the moon or anywhere else in the universe. Weight on the other hand is a measure of the pull of a planet i.e. Earth on the stuff contained in the object. The direction of the force of gravity is downwards towards the centre of the Earth.

a helicopter hovering in place

Fourth example: a helicopter hovering in place. How do you draw a helicopter? A box. What if you're tired of drawing boxes? A circle is a good alternative. What if even that's too much effort? Draw a small circle, I suppose. What if I want to try drawing a helicopter? Extra credit will not be awarded.You know the rest of the story. All objects have weight. Draw an arrow pointing down and label it. The helicopter is neither rising nor falling. What keeps it up? The rotor. What force does the rotor apply? A rotor is a kind of wing and wings provide lift. Draw an arrow pointing up and label it.The helicopter isn't sitting on the ground, so there is no normal force. It's not a hot air balloon or a ship at sea, so buoyancy isn't significant. There are no strings attached, so tension is nonexistent. In other words, stop drawing forces. Have I mentioned that knowing hen to quit is an important skill? If not, I probably should have.
As mentioned earlier when two objects interact they exert equal and opposite forces. The force that opposes the force of gravity in called the Normal Force. This is equal to the force of gravity and acts in an upwards direction (opposite to the downwards direction of the force of gravity). This is exerted by the surface upon which the object is positioned on. Therefore the force of gravity is the action force and the normal force is the reaction force.

FREE BODY FORCE DIAGRAMS Free-body force diagrams are used to give a clear and simple indication of the effect of the forces acting on an object. In a free-body force diagram only the forces acting directly on the object are shown. The forces are represented by arrows, the direction of the arrow gives the direction of the force and the size of the arrow represents the size of the force. This assists the reader in determining the net force acting on the object.

Units of Force

Force is a vector, it has both direction and magnitude. The SI unit for force is the newton (N). One newton of force is equal to 1 kg * m/s2. Force is also represented by the symbol F.

Force is proportional to acceleration. In calculus terms, force is the derivative of momentum with respect to time.

Describing a Force:

A force is a vector quantity. A vector quantity is a quantity which has both magnitude and direction. To fully describe the force acting upon an object, you must describe both its magnitude and direction. Thus, 10 Newtons of force is not a complete description of the force acting on an object. 10 Newtons, downwards is a complete description of the force acting upon an object.

(Note: What is the difference between vector and scalar quantities? A vector has both strength and direction, a scalar quantity can be described using only 1 quantity, magnitude. Examples of scalar quantities are: time, energy and volume since they only represent magnitude and no direction.

Solved Examples

Question 1: Aimmee is having a toy car of mass 2kg. How much force should she should put on the car so that it should move with the acceleration of 8m/s²?
Solution:

Given: Mass of toy car m = 2 Kg,
          Acceleration a = 8m/s²,
          Force to be applied by aimmee is given by F = m ×$\times$ a
                                                                           = 2 Kg ×$\times$ 8 m/s² 
                                                                           = 16 Kgm/s²
                                                                           = 16 N.

Derivation of Centripetal Force

Centripetal force holds a body in circular motion. Direction of this force is towards the center. And it is perpendicular to the velocity of the object. Simply we can say that, centripetal force keeps an object moving with constant velocity in a curved path. The mathematical proof was given by Christian Huygens in 1659. The derivation of centripetal force is given below:

The force of a moving body is given as

F = ma........(1)

From the figure, we can write the expression

PQ→$\overrightarrow{PQ}$ + QS→$\overrightarrow{QS}$ = PS→$\overrightarrow{PS}$
-v1$v_1$ + v2$v_2$ = Δv$\mathrm{\Delta }v$

Δv$\mathrm{\Delta }v$ = v2$v_2$ - v1$v_1$

The triangle AOB and PQS are similar. So

ΔvAB$\frac{\mathrm{\Delta }v}{AB}$ = vr$\frac{v}{r}$

AB = arc  AB = vΔ$\mathrm{\Delta }$ t

ΔvvΔt$\frac{\mathrm{\Delta }v}{v\mathrm{\Delta }t}$ = vr$\frac{v}{r}$

ΔvΔt$\frac{\mathrm{\Delta }v}{\mathrm{\Delta }t}$ = v2r$\frac{v^2}{r}$

a = v2r$\frac{v^2}{r}$

Substitute this value in (1) we get the centripetal force

F = mv2rv2r = mrω2