Problems on Law and Action and Reaction

Problem 1: A car with a mass of 1250 Kg traveling by an acceleration of 10 m/s² hits a bike. What force does the car experience?

Solution:

given , Mass(m) = 1250kg , acceleration(a) = 10m/s²

Using Newton’s second law F = ma:

F = 1250 x 10 = 12500 N

the force experienced by the car due to hitting the bike would be equal in magnitude and opposite in direction to the force experienced by the bike due to being hit by the car. However, the magnitude of the force experienced by the car is not equal to the acceleration; it’s equal to the mass multiplied by the acceleration. Hence, the car experiences a force of 12500 N.

Problem 2: A Dog of mass 10 kg jumps on a table of mass 60 kg. As the Dog walks around on the table, what is the average force that the table applies to the Dog? Use g = 10 m/s².

Solution: 

The force that the dog applies to the table is its weight. As per Newton’s third law, the table also applies a force to the dog of the same magnitude. 

The force on the dog from the table is:

F_s = F_N = ma = 10 kg × 10 m/s² = 100 N

Problem 3: A boy is riding his scooter and pushes off the ground with his foot. Thus this causes him to accelerate at a rate of 8 m/s². Boy’s weight is 600 N. What is the strength of his push off the ground? Use g = 10 m/s².

Solution:

Boy’s weight, F is 600 N.

The formula to calculate the force on an object is,

F = ma

where m is the mass and a is the acceleration. 

or

m = F / a

m = 600 N / 10 m/s²

m = 60 kg

Boy accelerates at 8 m/s². so, he is pushed by a force of

F = ma = 60 kg × 8 m/s² = 480 N

Problem 4: Two bodies apply forces to each other. The force on one of the bodies as a function of time in the x-direction is kt + b, where k and b are constants. What’s the force as a function of time in the x-direction on the other body? Consider no other forces are present besides the forces the bodies apply to each other.

Solution:

According to Newton’s third law of motion, the force exerted by one body on another is equal in magnitude and opposite in direction to the force exerted by the second body on the first. Therefore, if the force on one body in the x-direction is kt + b

then the force on the other body in the x-direction would be -kt-b This ensures that the forces between the two bodies satisfy Newton’s third law.

Law of Action and Reaction is the other name for Newton’s Third Law of Motion. There are three basic laws given by famous English Physicist Isaac Newton that are helpful in defining the motion of any object in an inertial frame of reference. The third law of Newton is also called the Law of Action and Reaction. As its name suggests, it explains, “For any action to an object, we have an equal and opposite reaction.”

This could be explained by the example that if we have a ball that strikes a wall with a force of F₁ (action force), and the wall applies a force of F₂ (reaction force), then the action force is always equal to the reaction force, i.e. F₁ = F₂

In this article, we will learn about Newton’s Third Law of Motion (Law of Action and Reaction), its Examples, and others in detail.