Interesting Facts

The following are some facts in nature. Think of the physical reasons for them:

(1) The center of the geometric shadow of a coin placed in front of a narrow source of light contains a bright   spot. This is called the Poisson Spot or Arago Spot or Fresnel Bright Spot.
(2) The moon's sky is black.
(3) The surface of mars is red.
(4) The pitch of the sound from the siren of an approaching ambulance is higher than that of a receding one. This is due to the phenomenon called Doppler effect.
(5)  Black-topped roads are seen covered with water on a hot summer day. This phenomenon is called mirage.
(6) A metal bar feels colder than a wooden one although they are in the same environment.
(7) A plastic ball keeps on floating if it is placed on the top a water fountain or on an air-jet. This can be explained by Bernoulli's Principle.
(8) A nitrogen cooled magnet floats on top of a superconductor. This is related to the phenomenon called the Meissner effect.
(9) A postcard placed on top of a glass filled with water will remain there if you gently turn it upside down holding up the postcard, and then remove your had carefully from the postcard.
(10) Sometimes you can see colorful lights at night time in the northern sky. This light is also called Aurora Borealis.

Friction

Friction is a force opposing the motion of an object when the object tends to move relative to the other. Therefore, it is an example of contact force.

Friction is zero when a block lies on a flat surface. If an external force is applied on the block and increased slowly, the friction between the block and the flat surface increases almost linearly. This friction is called static friction. The magnitude of this friction is always less than the product of the coefficient of friction between the two surfaces and the normal reaction on the block. The block starts sliding when the force reaches its threshold value. This friction (the friction at which the block is about to start) is called the limiting friction. The magnitude of this friction is always equal to the product of the coefficient of friction between the two surfaces and the normal reaction on the block. Once the block starts sliding, the friction drops and remains almost constant. This is called the kinetic or dynamic friction. Therefore, the maximum value of friction is the limiting friction.

Friction is a necessary evil. Friction causes the loss of energy into a non-renewable form (thermal energy), but at the same time we can not do several important things without friction. For example, walking is impossible without friction between our feet and the ground. 

The study of friction is called tribology.

Test Yourself: 

(1) A horse has to apply more force to start a wagon than to keep it into motion. Why?

Free body diagrams

A free body diagram is a force diagram which shows all the forces acting on an object. It is called a free body diagram because an object in question is separated from the environment counting all the forces acting on it, and NOT the forces it exerts on other objects. In a free body diagram, an object is usually represented by a rectangular block and the forces acting on it are represented by lines with arrows, the arrows showing the direction of force. 

Example: A book lying on the top of a table has two forces acting on it. They are -  the force that the earth acts on it in vertically downward direction (Gravity) and the force the table acts on the book in vertically upward direction (Normal Reaction). Therefore, the free body diagram of the book should contain a rectangular block with two equal arrows  passing through its center, one pointing  vertically upward and the other vertically downward.
Drawing a correct free body diagram of an object is extremely important step in the study of motion of the object because this helps us to apply Newton's Laws of motion accurately.

Test yourself


(1) You throw a ball from the top of a tower at an angle of thirty degrees above the horizontal. How many forces are acting on it right after the ball leaves your hand? Draw its free body diagram and apply Newton's Second Law of motion to describe its motion. You can neglect air friction in this case.

(2) How many forces are acting on an athlete (a) when he is about to jump?  (b) when he is in air after he makes a jump? Draw his free body diagram in each case.

(3) How many forces are acting on an object on a platform scale lying on the floor of an elevator under the following conditions?
(a) The elevator is at rest.
(b) The elevator is moving upward with a constant velocity.
(c) The elevator is moving downward with a constant velocity.
(d) The elevator is accelerating upward.
(e) The elevator is accelerating downward.
(f) The elevator is in free fall !
Draw a free body diagram in each case. Apply Newton's Second Law of motion to describe the motion of the object mathematically.

Newton's Laws of Motion

First Law of Motion: Everybody in the Universe continues in its own state of rest or of uniform motion along a straight line in the absence of an external force.

For example, a book lying on a table remains there unless a net external force acts on it.  A rolling ball on a flatland would  remain rolling forever if there were no friction between the ball and the ground. 

Newton's First Law of motion is also called Galileo's Law of Inertia. Why?  

An object on itself is inert. This means that a moving object tends to be in the state of motion and an object at rest tends to be at rest if no external force acts upon them. This property is called inertia of the object. The tendency of a moving object to be in the state of motion is called the inertia of motion. For example, passengers in a moving vehicle are thrown forward when the vehicle suddenly stops. It is because the lower part of the body of a passenger which is in contact with the vehicle comes to rest when the vehicle suddenly stops but the upper part of the body of the passenger tends to continue in the state of motion due to inertia of motion. Therefore, the passenger falls forward. On the other hand, the passengers are thrown backwards when a vehicle suddenly starts. The lower part of the body of passenger which is in contact with the vehicle suddenly comes to motion but the upper part tends to be in the state of rest due to inertia of rest. Therefore, the passenger falls backward.

Second Law of Motion: The rate of change of momentum of an object is directly proportional to the net force acting on the object, and it takes place in the direction of the force. 

Momentum of an object measures its total quantity of motion. Mathematically, it is the product of the mass of an object and its velocity. 

If an object is under the influence of net force, its velocity keeps on changing continuously. Therefore, the momentum of the object, which is equal to the product of its mass and velocity also changes with time. For a given time interval, the change in momentum of the object divided by the time interval is higher if the force is stronger and this change takes place in the direction of the net force acting on the object. 

Third Law of Motion: To every action, there is an equal and opposite reaction.

If an object exerts a force on an another object, the second object exerts exactly the same amount of force on the first object in the opposite direction. A very important point to note is that the action-reaction pair of forces always act on different objects, and they, in general do not cancel each other ! 

Summary:

(1) All the three laws of motion describe the same physical quantity - Force. 

(2) The First Law of Motion defines force, the Second Law of Motion measures force and the Third Law of Motion gives the property of force. 

Test Yourself:

(1)  A horse rider falls backward when the horse suddenly starts but falls forward when the horse suddenly stops. Why?

(2) An athlete runs through some distance before making a long jump. Why?

(3) A gun recoils while shooting. Why? 

(4) A roll of tissue unwinds without snapping if  the sheet of tissue is pulled gently but snaps into pieces if it is jerked. Why?

(5) It is difficult to walk in ice or sand. Why?

(6) Fruits fall when the branches are shaken. Why?

(7) If an object of one kilogram moving with a velocity of  one meter per second changes its velocity to two meters per second in two seconds, what is the net force acting on the object?

(8) There are a number of thick hardcover books nicely stacked on top of each other. You are asked to pull out a book from the middle of the stack without moving out other books. How do you do that?

(9) Put a postcard on top of a glass and a penny on the middle of the postcard. What happens to the coin if you pull the card horizontally (a) slowly (b) rapidly? Why?

(10) Place carefully a post card on top of a stick which is standing on a vessel filled with sand. If you hit the stick on its middle horizontally, the stick will fall out of the vessel, but the post card falls on the vessel itself. Why?
(11) "Newton's First Law of motion can be obtained from the Newton's Second Law of motion in a special case." Explain.