Mass, the fundamental property of every object, measures how much matter the body contains. Seeing its importance with different approaches and solved problems, this post will discuss how to find mass with acceleration and force.
Sir Isaac Newton offered a number of principles and theories that led to the development of several methods for estimating object mass. Newton’s Second Law is the simplest and most widely used method of calculating mass, as it involves the calculation of mass using both force and acceleration.
Let’s look at how Newton’s second law can help us in determining the mass of any object.
How to find mass with acceleration and force using Newton’s Second Law:
The terms mass, force, and acceleration are all used in everyday life and are related to one another. Force is a physical effect that causes an object’s state of motion to change, which means it either speeds up or slows down. Mass is a type of resistance that prevents an object’s state from changing due to force. As a result, the object will be able to alter its state of motion once the force overcomes this resistance.
The most general form of Newton’s Second Law states that the force acting on the body or particle will be equal to the rate of change of the body or particle’s momentum. Thus, putting this statement into a formula, it can be expressed as:
Where p is the object’s linear momentum. It is calculated as the product of the object’s velocity and mass. Thus, mathematically we can write its as:
p = mv
So, if the value of momentum is substituted in the force equation, we get:
When the velocity of an object approaches the speed of light, the mass of the object increases; however, this is not the case. Because the velocity of the object being evaluated is not very great, i.e. close to the speed of light, the mass does not change. As a result, only velocity varies with time, but the mass remains constant.
But differentiation of velocity with time gives acceleration.
As a result, force may be expressed in terms of mass and acceleration, and its mathematical representation is as follows:
F = ma
Newton’s Second Law is represented by this equation. This can be used to calculate the mass of an object by making it the subject of an equation. As a result, the mass of an object can be calculated as follows:
Newton, Kilogram, and m/s2 are the SI units of force, mass, and acceleration, respectively, according to the International System of Units.
The above mass equation reveals two facts, which are listed below:
- m ∝ F:- This proportionality shows that more mass requires more force, whereas smaller mass requires less force.
- m ∝ 1/a:- Because acceleration is inversely related to object mass, an object with a large mass will experience less acceleration, whereas an object with a low mass will experience more acceleration.
We can conclude from this that if the mass of an object is large, it will require a large external force, and because mass is essentially resistance, its acceleration will be law, and vice versa.
Assume you’re exerting force on both a toy and a real car. The toy car then accelerates without requiring much force. However, a real car requires more force to move forward. Or perhaps it doesn’t move at all. This is due to the fact that the mass of the toy car is less than that of the real car. As a result, the amount of force required to accelerate them varies.
Let us see some problems of finding mass using acceleration and force.
Problem: When a force of 6.0 newtons is applied to an object, it accelerates at 12.0 m/s2. Determine the object’s mass.
Force on object F = 6 N
Acceleration of object a = 12 m/s2
m = ?
Mass of the object:
∴ m = 2 kg
Thus, here, in this case, the mass of the object is 2 kg.
Problem: To accelerate a ball at 4 m/s2, it requires 24 N of force. What would be the object’s mass then?
Acceleration of ball a = 4 m/s2
Force applied on ball F = 24 N
m = ?
Mass of ball:
∴ m = 6 kg
Thus, to accelerate at 4 m/s2, a 6 kg ball requires 24 N of force.
FAQs on Finding mass using Newton’s Second Law:
Q.: State Newton’s laws of motion.
Ans: The statements of all three of Newton’s laws of motion are given below:
1st law: The state of a body does not change until the non zero net force does not operate on it, which means that if it is stationary, it will remain so, and if it is moving, it will maintain its speed. This is often referred to as the Law of Inertia.
2nd law: The rate at which a body’s momentum changes is proportional to the force applied to it. Or, to put it another way, the amount of acceleration of an object is proportional to the force applied to it and inversely proportional to the body’s mass. It can be written as follows in the form of an equation:
F = ma
3rd law: During the interaction of two bodies, the force exerted by both will be equal in magnitude and in the opposite direction.
Q: When a rocket is launched from its launching pad, it not only gains speed but also gains tremendous acceleration as the firing proceeds. What is the reason for this?
Ans.: When a rocket is launched, it accelerates as a result of the firing.
Because of the fuel used in rockets, firing from them is possible. The fuel in the rocket burns as it fires. As a result of the constant firing, mass is lost, and acceleration increases because mass and acceleration are inversely proportional.
Q: Explain how each of Newton’s laws influences a tug-of-war game.
Ans.: The importance of each Newton’s Law in Tug of War is listed below:
- Newton’s first law: Until the pulling begins, that is, until the force is applied, the rope will remain in the same position.
- Newton’s second law: The force of each team can be calculated using Newton’s second law. The force with which each team pulls is determined by the mass of each team’s body and the acceleration with which the rope moves.
- Newton’s third law: One team pulls the rope with force towards themselves, while the other team pulls the rope away from them. Both teams are essentially pulling opposite directions. As a result, until one side of the pull does not get high, neither team will win.
Q. Describe what happens if you try to push someone who is heavier than you. What if he pushes you back as well?
Ans: The body will accelerate only if the net force acting on it is greater than zero.
As the person you are attempting to push has a greater mass than you, he will need more force to accelerate than you can provide. As a result, the person will remain static. Because your mass is smaller than his, when he pushes you back, you will accelerate in the direction of the push.
We saw how to find mass without acceleration in the previous post and how to find mass with acceleration and force in this one. We hope that these posts have answered your questions.