FORCES!
Introduction:
Hello
everyone! Hope you all are having a good day. Today we are going to start a new
chapter and that is “forces”. We all are familiar with what a force is, right?
Okay, let’s say your car’s wheel got punctured in the middle of..nowhere. What
will you do? You will push the car to make it move somehow. In this case, you
are applying a force to make the car move. Here: we defined a force!
Definition:
So
simply, a force is a push or pull that an object exerts on the other. It
produces or tends to produce motion (let’s say you push a wall, you are
applying force but the wall does not move) or else, it stops or tends to stop
motion. The SI unit of force is Newton (N). A force of one newton is roughly
the amount of force with which the Earth’s gravity pulls an object of 0.1 kg
i.e. 100g. Force is a vector quantity, which means it has a direction too. (We
have already discussed scalar and vector quantities in detail in the tutorial
on kinematics). We’ll discuss more about forces in this tutorial.
Addition of Vectors:
When
we add two vectors, we have to consider the direction, unlike in scalars. As
for scalar quantities we simply add up the magnitudes e.g. a weight of 50g and
20g gives a total of 70g. When we add up two vectors, we are actually trying to
find a single vector which will produce the same effect as the two vectors
added together. This single is called a resultant vector.
1.
Addition of parallel vectors:
Okay
in the above case, two parallel forces are acting on an object. How will we
find the resultant? It’s easy. First see if the forces are acting in the same
direction or in opposite direction. We can see the forces are in opposite
direction: the 40N force is acting upwards while the 25N force is acting
downwards. So the resultant force in this case is 15N upwards: 40N -
25N. (Remember to state the direction while mentioning a vector quantity).
Observe
the following summation of two parallel forces:
It
makes it more clear, right? Good then, let’s move on!
2.
Addition of non-parallel vectors:
Now
what to do with such questions?
We
have all studies the Pythagoras’ Theorem in math, which goes like this:
Here’s
how we’ll solve the big problems:
Now,
does this make it clear? We’ll simply form a right angled triangle, apply the
Pythagoras’s theorem and we have the resultant force! But how will we state the
direction of the resultant in a written form?
Here!
Now we can easily write down the direction: the resultant is 15.6 N acting 45° anticlockwise.
Not that of a big question, is it? Wait, are you all familiar with the
trigonometric ratios: sin, cos, tan? Hmm, if not, here we go:
Okay,
so you might be asked to find the resultant by drawing a scaled vector diagram.
Not difficult at all. Just follow the steps!
Here,
we have formed a parallelogram and found the resultant. We have to take a scale
first, let’s say 1 cm on paper represents an actual of 10N. We’ll measure the
length of the resultant and using the scale, will determine the actual
magnitude. Easy as that.
Forces and Zero Acceleration:
Let’s
say a car is moving with a constant velocity. It means that the acceleration is
zero. However, even though acceleration is zero, it does not mean that there
are no forces acting on the car, it means, in fact, that the forces are
balanced. So we can conclude that for an object with zero acceleration, the
different forces acting on it are balanced or add up to zero-i.e. the resultant
net force is zero.
Newton’s First Law of Motion:
The
situation we just discussed brings us to Newton’s first law of notion which
states:
Every object
in a state of uniform motion tends to remain in that state of motion unless an
external force is applied to it.
Newton’s Second Law of Motion:
When a
resultant force acts on an object of constant mass, the object will accelerate
and move in the direction of the resultant force.
The
relationship between an object's mass m, its acceleration a, and the
applied force F is F = ma. Acceleration and force
are vectors; in this law the direction of the force vector is the same as the
direction of the acceleration vector.
Try
solving this and see if you can:
Q1: Mike's
car, which weighs 1,000 kg, is out of gas. Mike is trying to push the car to a
gas station, and he makes the car go 0.05 m/s2. How much force is
Mike applying to the car?
The
formula F = ma can also be written as W = mg, because W i.e. weight is a force
with SI unit Newtons. And g is acceleration due to gravity.
Newtons Third Law of Motion:
For every
action, there is an equal and opposite reaction.
Okay so let’s study
how a rocket works to understand the Newton’s third law!
The
rocket's action is to push down on the ground with the force of its
powerful engines, and the reaction is that the ground pushes the rocket
upwards with an equal force. Easier now?
Answers:
Q1: 50N
