Laws of Motion Numericals

Laws of Motion describe how objects move under the influence of different types of forces. These forces can be due to any physical phenomenon, but their effect is the same. All the forces change the momentum of the system on which they are acting. Newton gave three laws, these laws describe the interaction between two objects and the forces between them. These laws become the building block for the further theory of mechanics and motion. Let’s look at these concepts and some problems with them.

Newton’s Laws of Motion

Sir Isaac Newton was an English physicist and mathematician who gave the three laws of motion called Newton’s Law of Motion which formed the base for classical mechanics. These laws still keep giving accurate predictions except for bodies traveling with speeds comparable to light or the size of an electron. These were the first laws that described the forces acting on the bodies and the motion of the body which is governed by these forces. There are three laws of motion that are given by Sir Issac Newton that include,

• Newton’s First Law of Motion
• Newton’s Second Law of Motion
• Newton’s Third Law of Motion

Now let’s learn about these laws further in this article.

Newton’s First Law (Law of Inertia)

Newton’s First Law of motion also called the law of interia states that if a body is at rest or is moving in a straight line with constant speed. It will keep moving in a straight line at constant speed or will remain at rest until it is acted upon by an external force. This property of any object to resist a change in its state is called inertia and thus this law is known Law of Inertia.  

Newton’s Second Law

Newton’s Second Law is a quantitative description of the changes that take place when an external force acts on the body. The momentum of the body is defined as the product of the mass and velocity of that body. When a force acts on the body, it brings about changes in the momentum of the body or its direction, or both. It is one of the most important laws in the field of classical mechanics. Assuming the mass of the body is “m”, the law is given by,

F = ma

Here, F is the force acting on the particle, and “a” denotes the acceleration produced in the body. The direction of acceleration is the same as the direction of motion.

Newton’s Third Law (Law of Action and Reaction)

Newton’s Third Law also called law of action and reaction states that when two bodies interact with each other, they apply forces to one another which are equal in magnitude and opposite in direction. This law is also known as action-reaction law. It allows us to explain phenonmenon such as static equilibrium, where all the forces are balanced, but it also applies to bodies in uniform or accelerated motion. If the net forces acting on the body are equal, the body is said to be in equilibrium.

Examples on Newton Laws of Motion

Example 1: Calculate the momentum of a ball thrown at a speed of 10 m/s and weighing 800 g.

Solution:

Given,

• M = 800 g
• V = 10 m/s

Momentum is given by,

p = MV

Plugging in the values in the formula

p = MV

p = (800)(10) 

p = 8000 gm/s

p = 8 × 10³ gm/s

Example 2: Calculate the momentum of a ball thrown at a speed of 10 m/s and weighing 20 g.

Solution:

Given,

• M = 20 g
• V = 10 m/s

Momentum is given by,

p = MV

Plugging in the values in the formula

p = MV

p = (20)(10)

p = 200 gm/s

p = 2 x 10² gm/s

Example 3: A force of 20N is acting on a body of mass 2Kg. Find the acceleration produced.

Solution:

Given,

• m = 2 Kg
• F = 20 N

Acceleration will be given by,

F = ma

Plugging in the values,

F = ma

20 = (2)(a)

10 m/s² = a

Example 4: A force of 100N is acting on a body of mass 5Kg. Find the acceleration produced.

Solution:

Given,

• m = 5 Kg
• F = 100 N

Acceleration will be given by,

F = ma

Plugging in the values,

F = ma

100 = (5)(a)

20 m/s² = a

Example 5: A body of 2 kg is moving at a velocity of 50m/s. A force starts acting on it and the velocity becomes 20m/s in a time of 5 seconds. Find the force applied to the body.

Solution:

Given,

• m = 5 Kg
• v_i = 50 m/s
• v_f = 20 m/s
• t = 5 s

Force is defined as the rate of change of momentum.

F = m(v_f  – v_i)/t

F = (5)(50 – 20)/(5)

F = 30N

Example 6: A body of 10 kg is moving at a velocity of 100m/s. A force starts acting on it and the velocity becomes 20m/s in a time of 10 seconds. Find the force applied to the body.

Solution:

Given,

• m = 10 Kg
• v_i = 100 m/s
• v_f = 20 m/s
• t = 10 s

Force is defined as the rate of change of momentum

F = m(v_f  – v_i)/t

F = (10)(80 – 20)/(10)

F = 80N

Example 7: The momentum of the body is given by the equation below,

p(t) = 3t² + 4t + 5

Find the force acting on the body at t = 5.

Solution:

Force rate of change of momentum,

F = dp/dt

Given,

p(t) = 3t² + 4t + 5

F = dp/dt = d/dt(3t² + 4t + 5)

F = 6t + 4

At t = 5

F = 6(5) + 4

F = 34 N

Thus, force acting on the body at t = 5 sec is 34 N.

Example 8: The momentum of the body is given by the equation below,

p(t) = e^t + t² + 20

Find the force acting on the body at t = 0.

Solution:

Force rate of change of momentum,

F = dp/dt

Given,

p(t) = e^t + t² + 20

F = dp/dt

F = d/dt (e^t + t² + 20)

F = e^t + 2t

At t = 0

F = e⁰ + 2×1
   = 1 + 2
   = 3

F = 3 N

Thus, the force acting on the body at t = 0 is 3 N.

Numericals on Laws of Motion

Lets learn Law of Motion Numericals for class 9 and class 11

1. If the momentum of any body is, p(t) = 3t³ + 5t² + t. Find the force acting on the body at t = 2.

2. If the distance covered by an object is given by, d(t) = t³ + t. Find the acceleration on the body at t = 3.

3. If the distance covered by an object is given by, d(t) = 4t⁴ + 3t + 5. Find the velocity on the body at t = 0.

4. A body of 19 kg is moving at a velocity of 100 m/s. A force starts acting on it and the velocity becomes 120 m/s in a time of 10 seconds. Find the force applied to the body.

5. Force acting on body is 120 N, the mass of the body is 12 Kg. Find the acceleration produced produced by the body.

FAQs on Laws of Motion

1. Who Discovered the Laws of Motion?

The laws of motion were discovered by Sir Isaac Newton an English Mathematician.

2. What is Law of Inertia?

Law of Inertia is also called the Newton First Law of Motion. This law states that an object at the state of rest or at the state of motion stays in its state until an external force is applied.

3. What is Law of Action and Reaction?

Law of Action and Reaction is the other name of Newton Third Law of Motion. This law states that, “Every action has its equal and opposite reaction.”

4. What is Formula for Force Acting on a Body?

The force acting on a body is given using the formula,

F = ma

where,

• m is Mass of Object
• a is Acceleration of Object

5. What is Formula for Momentum of a Body?

The momentum of an object is given using the formula,

F = mv

where,

• m is Mass of Object
• v is Velocity of Object