DiscussForce and Laws of Motion
To understand force, we first need to understand mass and inertia. Actually, mass and inertia are interconnected in a way – the more mass a body has, the more inertia it has. Inertia can be thought of as the “unwillingness” of a body to change its motion – either state of rest, or motion at constant velocity.
Eg. A body with mass 10 kg has twice the inertia of a body with mass 5 kg.
NOTE: From a physics point of view, motion at constant velocity has some similarities with state of rest.
Force can be thought of as “the effort put in to change the motion of a body”. This includes making the body move faster, slower, or change its direction. Consider the following images that demonstrate this:
Question: What else can force do to a body, besides affecting its motion?
A force can also deform a body, that is, change its shape or size, compress or elongate it. Following is a pictorial representation of these changes. Note that these changes do not constitute motion, so we’ll not discuss about them in this chapter.
Recall that acceleration is a vector quantity, that is, it has magnitude and direction. Now, if we define Force as:
Force = mass x acceleration
It is easy to see that Force is a vector quantity, as it is simply acceleration (a vector) multiplied by mass (a scalar). This implies that force also has both magnitude and direction. This makes sense because, we expect a body to move in the direction in which the force is applied.
Friction
Friction arises due to the roughness between two surfaces, and it tries to oppose relative motion between the two surfaces. An interesting property of friction is that it is a self-adjusting force.
Question: Imagine there is a heavy book on a wooden table and you apply a small force to it sideways. Will it move?
The book will probably not move. But what’s interesting in this scenario is, when you apply a small force, friction arises to counter your applied force. This friction was not present before you tried to move the book. And, it is equal and opposite to the force you are applying.
This is what self-adjusting means: friction adjusts its value to exactly match the force it is trying to counter.
Question: If you keep increasing the force applied by you on the book, will it move?
Yes. This is because friction can only increase up to a maximum value (which depends on the two interacting surfaces- the book’s face touching the table and the table’s surface, and the mass of the book). If you apply more force than this maximum value, friction cannot counter your force and the book moves. Note that friction doesn’t disappear at this point: its value stays constant at the maximum.
X is the direction of the force applied by you. Y is the direction of friction.
Laws of motion
First law of motion: An object remains in a state of rest or of uniform motion in a straight line unless compelled to change that state by an applied force.
We have already discussed this while defining force and inertia, in fact; the first law of motion provides a way to define force. Also, since the law talks about the tendency of an object to stay at rest or move at constant velocity, it is also known as “the law of inertia”. The larger the mass of the object, the larger is the force required to change its state of inertia.
Question: Give an example from daily life where you have felt the first law of motion in effect.
The first law is applicable everywhere! Every time you move something that wasn’t moving, (say, pick up a bottle for drinking water) or flip a page of a book, or write with a pen, you are moving things by applying a force on them, thus, changing their previous state of inertia.
Momentum: Momentum is the product of mass and velocity of an object. It is a vector quantity, denoted by p. Thus, p = mv, where m stands for mass and v for velocity. The unit for momentum is kg m/s.
The second law of motion qualitatively defines force. If the mass of an object does not change with time, the rate of change of momentum is simply mass times acceleration, which gives force F:
F = ma
The units of Force are kg m/s2. To honour the great scientist Issac Newton, the unit kg m/s2 is also called Newton, and denoted by N.
Second law of motion: The second law of motion states that the rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of force.
Question: What are some consequences of second law of motion, which we see in everyday life?
Again, similar to the first law, there are examples everywhere. We know that even a slow moving bus can hurt a pedestrian, but a slow moving pebble cannot. This is because even for the same velocity, the bus has greater mass and hence, greater momentum. So, in order to have the any lethal effect, the pebble needs to compensate by having greater velocity, which is what happens when you fire a bullet from a gun – despite the small mass of the bullet, its high velocity means it has a large momentum.
In the previous example, we talked how a bullet fired has a large momentum, but to have any kind of effect on a body, you need force, not momentum. How does this momentum “translate” to force?
This question is answered by the third law of motion.
Third law of motion: To every action there is an equal and opposite reaction.
However, it must be remembered that the action and reaction always act on two different objects, simultaneously.
Simply put, this means every force applied on a body produces a reactionary force on the agent applying the force. Let us understand this better with the bullet example.
We know that a fired bullet has a huge momentum.
When it comes in contact with a body at rest, the body tries to reduce the velocity, and hence, the momentum of the bullet.
In order to change the momentum of the bullet, the body has to apply a force the bullet. Since the body tries to reduce the momentum in a very short time, the rate of change of momentum is large, which is nothing but the force applied on the bullet by the body.
By the third law of motion, the bullet applies an equal and opposite force on the body.
Conservation of momentum
Consider a physical system (a set of bodies). Suppose that the system has some initial momentum u, and no force is applied on this system.
Question: Do you expect the momentum of the system to change?
No. Since an external force is required to change the momentum of a particle, object or system, we conclude that the momentum of the system should remain constant. This follows directly from the second law of motion, which states that change in momentum is caused by an external force. Hence, in the case where there is no external force, there is no change in momentum. This is precisely what the principle of conservation of momentum is.
Question: Give examples of conservation of momentum from daily life.
If you have ever ice skated, you must have noticed you can move long distances over ice without much effort, this is because the friction on ice is very less, which is the only external force exerted on your body. Since the external force is negligible while ice skating, your momentum is preserved and you can go long distances without applying any force.
Summary
First law of motion: An object continues to be in a state of rest or of uniform motion along a straight line unless acted upon by an unbalanced force.
The natural tendency of objects to resist a change in their state of rest or of uniform motion is called inertia.
The mass of an object is a measure of its inertia. Its SI unit is kilogram (kg).
Force of friction always opposes relative motion of objects.
Second law of motion: The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force.
The SI unit of force is kg m s–2. This is also known as newton and represented by the symbol N. A force of one newton produces an acceleration of 1 m s–2 on an object of mass 1 kg.
Third law of motion: To every action, there is an equal and opposite reaction and they act on two different bodies.
In an isolated system (where there is no external force), the total momentum remains conserved.