Graph of Force Vs Mass - JEE Important Topic

The graph force vs. mass indicates acceleration. A force is said to be applied when an object pushes or pulls. The interaction of the objects produces push and pull. Force is an external agent that has the power to alter a body's resting or moving position. It has a direction and a magnitude. The direction of the force is in the same direction the object moves. The graph of force vs. mass can be determined by Newton’s second law of motion, which is discussed in brief in the latter part of the article.

What is Acceleration?

If an object's velocity changes, it is said to have been accelerated. An object's velocity can alter depending on whether it moves faster or slower or in a different direction. Since acceleration has both a magnitude and a direction, it is a vector quantity. Additionally, it is the first derivative of velocity with respect to time and the second derivative of position with respect to time. A falling apple, the moon orbiting the earth, and a car stopped at a stop sign are a few instances of acceleration.

What is Mass?

In Physics, mass is a quantitative measurement of inertia, a basic characteristic of all matter. It is, in effect, the resistance that a body of matter offers to a change in its speed or position upon the application of a force. The mass of an object is a measurement of its matter content. A rubber ball weighs less than a lead ball of the same size because it has fewer particles, atoms, and the protons, neutrons, and electrons that make up the atoms. The mass of electrons is very small in comparison to protons and neutrons. The average mass of an atom is called an atomic mass.

Newton’s First Law of Motion

Newton’s first law states that “An object at rest remains at rest, or if in motion, remains in motion at a constant velocity unless acted on by a net external force.” This law is also known as the law of inertia. When the body is at rest, then velocity (v = 0) and acceleration (a = 0) indicate that the body will continue to be at rest.

Relationship Between Mass and Force 

Newton's second law of motion states that the force applied on a body is directly proportional to the rate of change of momentum. It means when a larger force is applied, the rate of linear momentum will be faster. Let us consider a body with mass “m” moving with velocity ‘v’. Now, the linear momentum of the body is written as:

p = mv

Now applying Newton’s second law of motion, 

$F\propto \dfrac{dp}{dt}$

$F=k\dfrac{dp}{dt}$

$F=k\dfrac{d\left( mv \right)}{dt}$

$F=km\dfrac{dv}{dt}$

$F=kma$

Where the value k experimentally is equal to 1

So, $F=ma$

Where ‘a’ is the acceleration of the body.

The acceleration would increase as the force did. When you push an item with a specific force, it accelerates with direct proportion to the force and indirect proportion to the mass of an item. A large force with a small mass causes a fast acceleration, while a small force with a large mass causes a gradual acceleration. Zero force applied to any mass results in zero acceleration.

Graph of Force vs. Mass

It can be a straight line that is inclined to the mass axis and whose slope indicates the constant acceleration. However, a curve of any polynomial function could be introduced with any variable acceleration. If the acceleration is constant, the graph is as follows:

Graph of Force v/s Mass

For a 1D body, the graph of force per unit length will be similar to the above graph.

What is Impact Force?

Any time when there is a change in momentum, there is said to be an impact force present. Impact forces have the power to damage an object and change its original shape. To lessen the likelihood of damage and injuries, it is necessary to lower the impact forces as much as possible. The magnitude of the force is equal to the product of mass and acceleration, according to Newton's second law of motion. This allows for a simple calculation of the impact force, which is equal to the change in momentum divided by the time required for the change. Therefore, the mass or the velocity can be decreased to lessen the impact force. The graph of force of impact will be an increasing decreasing type.

Examples of Impact Force

• Bungee Jumping: The elasticity of the rope helps in increasing the time with which the momentum changes. As a result, the jumper experiences less impact force, and the likelihood of an accident is lower.

• Smashing Egg: An egg dropped on a floor immediately cracks upon making contact with the hard surface. This occurs because when an egg is thrown with a certain velocity, it develops a momentum that is disrupted when it hits a barrier. It can be broken apart by the strong impact force caused by the quick shift in motion.

• Catching a Ball: The player pushes his hands backwards as soon as the ball touches his hands. By doing this, the player prolongs the period of time during which the ball's momentum changes, decreasing the force of impact.

• Safety Helmets: The cushioned inner surface of the helmet is compressed during a collision, which permits the velocity to alter gradually. The impact force is reduced, and the rider avoids fatal damage because of the longer time needed to alter the momentum.

• Long Jump: Long jumpers typically land in sand pits rather than on hard surfaces. This is due to the sand's ability to ensure the least amount of deceleration. The likelihood of harm decreases with decreasing deceleration values.

Conclusion

An object, from protons and electrons to planets and galaxies, can exert force on another object by pulling or pushing it. The only source of acceleration is a change in speed. Positive acceleration occurs when an object picks up speed, while negative acceleration occurs when an object loses speed. A measurement of an object's matter content is its mass. Newton's second law of motion states that acceleration is proportional to applied force, assuming that the mass is constant. If an object experiences a force due to impact, it has experienced an impact force. This indicates that an impact force has a very short duration and creates significant acceleration.