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Prove that F = ma
By BYJU'S Exam Prep
Updated on: September 25th, 2023
The force exerted on a system must be equal to the time rate at which its momentum is changing, according to Newton’s second law of motion. The formula of newton’s second law: f = m a. An illustration of Newton’s second law of motion:
Now we have To prove:
F = m a
According to newton’s second law force is given by,
F = dP/dt
But P = mv
Substituting the values
So F = d (mv)/dt
F = m.a [As a = dv/dt]
Table of content
Types of Force
An object’s state of motion or dimensions can change as a result of force, a physical cause. The push or pull on a mass-containing item changes its velocity. Based on their uses, forces can be divided into two categories:
- Contact forces are defined as forces that affect a body directly or indirectly through a medium.
- Non-contact forces are those that operate through voids without coming into physical touch with the body.
Applications of Newton’s Second Law
- Kicking a ball
We use force in a precise direction when we kick a ball. The force we provide to the ball increases as we kick it harder, which causes the ball to move farther.
- Pushing a cart
In a grocery store, an empty cart is simpler to maneuver than one that is filled, and heavier loads call for greater acceleration.
- Two people walking
If there are two persons walking, and one of them is heavier than the other, the slower-moving person will walk because they are moving more quickly.
Therefore, proved.
Summary:
Prove that F = ma
It is proved that F = ma. Newton’s second law of motion states that the force acting on a system must be equal to the rate at which its momentum is changing over time. The various applications of this law include two people walking, pushing a cart, and kicking a ball.
