Physics // Motion // Newton’s Law// PTK -Exams

 

Physics 

     Q1. Who discovered the three laws of motion?

    Ans: Sir Isaac Newton discovered the three laws of motion. 

Motion 

Rest & Motion

To specify the position of any object, it has to be mentioned with respect to a reference point.

If an object changes its position with respect to an origin, then the object is in motion with respect to that origin. 

 

Q.1. What is motion?

Ans: Motion is a change in position of an object with respect to time and its reference point.

Ex. A car from one place to another place....

                                              🚗  ..................> 🚗.........>

             reference point   

Types of motion:

1. Linear Motion: 

If anything moves along a straight line then its motion is called linear motion.

2. Circular Motion:

When a body rotates about a particular point or a line, keeping the distance of the particles of the body unchanged, it is called circular motion.          

3. Translational Motion:

If an object moves in such a way that all the particles of the object travel the same distance, at the same time, in the same direction then its motion is called translational motion. 

Ex. Plane has to move from every point of the plane travelling equal distance the same direction.

4. Periodic Motion:

If the motion of a moving object is such that it passes repeatedly through a definite point in the same direction in the same manner in a definite interval of time, then this motion is called a periodic motion.

Ex. Motion of the blades of a fan.

5. Simple Harmonic Motion:

Simple harmonic motion is a special type of periodic motion where the resting force on the moving object is directly proportional to the magnitude of the object's displacement and acts towards the object's equilibrium position.

Differences between distance and displacement

Distance                                                            Displacement

1. It is a magnitude that measures the length that is traveled by an object from one point to another.

1. It is a magnitude that measures the variation of the position of a body between two points, considering a starting point and an endpoint.

2. It is considered a scalar magnitude.

2. It is considered a vector magnitude.

3. It depends on the path that the object follows.

3. It does not depend on the path that the object follows.

4. It is expressed by a number and a unit of magnitude frequently in meters. 

4. In physics, it is expressed by a module (value), unity, direction, and meaning.

5. It is obtained from the sum of all the lengths traveled by an object.

5. It is obtained from the difference in the length value of an endpoint and an initial point of an object.

Difference between speed and velocity :

           Speed                                                        Velocity

1. Speed is the distance covered by a body in unit time.  

1. Velocity is the displacement covered by a body in a unit of time.

2. It is a scalar quantity.  

2. It is a vector quantity.

3. It Determines “How fast an object is moving”?  

3. It determines “In which direction an object is moving”? 

4. It indicates the rapidity of objects.  

4. It indicates both the rapidity and position of the object. 

5. It is the rate of change of distance.  

5. It is a rate of change of displacement.

6. It cannot be negative.  

6. The velocity of moving Objects can be negative, positive or can be zero.

 

 Equations of Motion:

Q.1. The velocity of a car is increased by 60 km/h in 1minute starting from rest. What is its acceleration?

v = at

v = 60km/h

= 60 x 1000 / 60 x 60

= 16.67 m/s

t = 60 s

a = u-v / t

= 16.67/60 m/s2

= 0.278 m/s2  Ans.

Q.2. A car is moving with a velocity of 60 mile/h, suddenly its engine stops. It takes 5 minutes to come at rest. What is the deceleration of the car?

The final velocity of the car, v = 0

We know,

1 mile = 1.6 km

 = 1600m

u = 60 miles/h

= 60 x 1.6 x 1000m / 60 x 60

= 26.8 m/s

Acceleration,   a = v - u/t

               = 0 - 26.8 m/s/60 s

= - 0.089  m/s2 

Thus the acceleration of the car  - 0.089 m/s2

deceleration   0.089  m/s2  Ans.

Q.3. The velocity of a bullet is 1.5 km/s. It has penetrated 10 cm of a wall. What is deceleration of the bullet?

v2    = u2  - 2as

v = 0
0 = (1.5  x 1000 )2 - 2a (10/100)2
a = (1.5 x 1000)2 / 0.2
= 11,250,000 m/s2 Ans.

Laws of Falling Bodies:

Q.1. A good bowler of cricket can throw a ball with a velocity of 150km/h. If he throws the ball vertically upwards, how high will it go?

150  km/h   = 150 x 1000 / 60 x 60

                   = 41.67 m/s

Acceleration due to gravity will act as retardation when the ball is thrown vertically upwards. the ball eventually comes to a stop. If the height is expressed by h then,

v = 0,                    u = 41.67 m/s

                           g = 9.8 m/s2

                           v2 = u2 - 2gh

h = u2/2g           = (41.67)2 / 2x 9.8  m

                        = 88.59 m

 

Newton’s laws of motion:

Sir Isaac Newton FRS (25 December 1642 – 20 March 1726/27)[a] was an English mathematician, physicist, astronomer, alchemist, theologian, and author who was described in his time as a natural philosopher.

Q. What are Newton's Laws of Motion?
Ans:  An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force.

Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:

A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force.
When a body is acted upon by a net force, the body's acceleration multiplied by its mass is equal to the net force.
If two bodies exert forces on each other, these forces have the same magnitude but in opposite directions. 

Newton’s first law: 

the law of inertia

Newton’s first law states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force. In fact, in classical Newtonian mechanics, there is no important distinction between rest and uniform motion in a straight line; they may be regarded as the same state of motion seen by different observers, one moving at the same velocity as the particle and the other moving at constant velocity with respect to the particle. This postulate is known as the law of inertia.

Newton’s second law: F = ma

Newton’s second law is a quantitative description of the changes that a force can produce on the motion of a body. It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it. The momentum of a body is equal to the product of its mass and its velocity. Momentum, like velocity, is a vector quantity, having both magnitude and direction. A force applied to a body can change the magnitude of the momentum or its direction or both. 

Newton’s second law is one of the most important in all of physics. For a body whose mass m is constant, it can be written in the form F = ma, where F (force) and (acceleration) are both vector quantities. If a body has a net force acting on it, it is accelerated in accordance with the equation. Conversely, if a body is not accelerated, there is no net force acting on it.

Newton’s third law:
 the law of action and reaction

Newton’s third law states that when two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction. The third law is also known as the law of action and reaction. This law is important in analyzing problems of static equilibrium, where all forces are balanced, but it also applies to bodies in uniform or accelerated motion. 

The forces it describes are real ones, not mere bookkeeping devices. For example, a book resting on a table applies a downward force equal to its weight on the table. According to the third law, the table applies an equal and opposite force to the book. This force occurs because the weight of the book causes the table to deform slightly so that it pushes back on the book like a coiled spring.

1. Suppose a bike with a rider on it having a total mass of 63 kg brakes and reduces its velocity from 8.5 m/s to 0 m/s in 3.0 seconds. What is the magnitude of the braking force?

Solution:
The combined mass of the rider and the bike = 63 kg
Initial Velocity = 8.5 m/s
Final Velocity = 0 m/s
The time in which the bike stops = 3 s

The net force acting on the body equals the rate of change of an object’s momentum.

The momentum of a body with mass m and velocity v is given by  p = mv

Hence, the change in momentum of the bike is given by

Hence, the net force acting on the bike is given by

Substituting the value, we get

The magnitude of the braking force is -178.5 N.

2. Calculate the net force required to give an automobile of mass 1600 kg an acceleration of 4.5 m/s2.
We calculate the force using the following formula.

                     F = ma

Substituting the values in the equation, we get

                   F = ma
                      = 1600 kg x  4.5 m/s2
                      = 7200 N

PTK Exams

Force and Motion

Force and motion are intimately intertwined concepts because a force is required to change an object’s motion. To get anywhere in understanding concepts in motion, you must first understand the terminology. Be careful here. As is typical in science, familiar words are used with very specific meanings that are different from their everyday meanings. Don’t assume that because a word is familiar that you know its meaning in this context.

What is the Difference between Speed and Velocity?

Speed and velocity are not the same thing even though they are often used as interchangeable terms. The basic difference is that velocity includes the direction of motion while speed does not. When you are driving, the speed of your car might be 50 miles per hour; its velocity might be 50 miles per hour towards the east. If in the same situation, we look at your velocity toward the north, the result is very different. The speed of the car is still 50 miles per hour, but your velocity is zero! The reason for this is that the direction part of the velocity is all toward the east and nothing is directed toward the north. Velocity requires both magnitude and direction.

An acceleration is a change in the velocity over a period of time. Specifically, acceleration is defined as the time rate change of velocity (a = v/t). You may be used to thinking of accelerating as speeding up, but it also includes slowing down and changing direction. Like velocity, acceleration is a vector quantity that also includes the direction. An acceleration perpendicular to the velocity will change the direction of the velocity without changing the speed.

Acceleration, velocity, and speed are all rates of change. Velocity and speed measure the rate at which the position changes, while acceleration measures the rate at which the velocity changes.

Hence the average speed over an interval is defined as the change in position, or displacement, during that time. If it takes you an hour to drive to a town 50 miles away, your average speed will be 50 miles per hour. If the town is east of your home, your average velocity will be 50 miles per hour toward the east.

The average acceleration is defined in a similar way. It is the change in velocity during a time interval divided by the time interval.

Question

1. If a 2,500-mile cross-country flight takes 5 hours, what is the average speed of the plane?

a) 12,500 miles per hour

b) 2,000 miles per hour

c) 500 miles per hour

d) 200 miles per hour

How are Velocity and Acceleration Represented Graphically?

Both can be represented on a graph as the slope of a line. On a graph with time as the x-axis (horizontal) and position as the y-axis (vertical), a constant velocity will be represented by a straight line, and the slope will be the value of the velocity or speed. A steeper slope indicates a higher velocity. If the line is curved, then the velocity is changing. In a similar fashion, a graph with velocity as the y-axis and time as the x-axis will show the acceleration.

What Causes Acceleration?

In order to have acceleration, there must be an unbalanced force applied to an object. This statement is the essential meaning of Newton’s first law. If there are no unbalanced forces acting on an object, that doesn’t mean the object is at rest. The object could be moving at a constant velocity. Macroscopic forces that we experience include gravity, friction, electromagnetic forces, and contact forces such as pushing on a surface.

Think about the following:

A box is sliding across the floor. When you stop pushing the box—applying a force—the box slows to a stop because there is no longer a force acting on the box.

air resistance slows the box down.

an object can move only when a force is acting on it.

the friction from the floor acts on the box against its motion to change its velocity.

Friction is the key here.

Objects do not need to have a force acting on them in order to keep moving. They only need the force to accelerate them (change their velocity). The frictional force of the floor accelerates the box in the direction opposite its velocity, so it slows to a stop.

How is Pressure Related to Force?

Pressure is force divided by area. A sharp knife cuts food more easily than a dull one because with a sharp knife, the same force is applied to a smaller area. Hence you can exert more pressure with a sharp knife than a dull one. We also feel pressure from air, water, and other fluids. This pressure increases with depth. So atmospheric pressure at sea level is greater than on a mountaintop. Similarly, when we dive to the bottom of a swimming pool, we feel a greater water pressure at a greater depth.