Definition of Force and Acceleration
Force is an agent acting externally and is capable of changing the state of rest or motion of a particular body. It is also defined as the push or pull on an object which has a certain mass and causes the object to change its velocity. Every time two things interact, a force is exerted on each of them. The two items no longer feel the force after the interaction ends. Forces occur exclusively as a result of interactions. A force can affect a body in three ways. (a) It has the ability to alter a body's speed. (b) It has the ability to modify the direction of a body's motion. (c) It has the ability to alter the shape of a person's body.
For the sake of simplicity, all forces (interactions) between objects can be divided into two groups:
forces of contact
forces generated by long-distance action
Contact Forces – When two interacting items are considered to be physically engaging each other, contact forces occur. Frictional forces, tensional forces, normal forces, air resistance forces, and applied forces are all examples of contact forces.
Action-at-a-distance forces are those that occur even when two interacting objects are not physically in contact with each other but can nevertheless produce a push or pull despite their physical separation. Despite their great spatial separation, the Sun and planets, for example, exert a gravitational attraction on each other.
Examples of contact and action-at-distance forces are listed in the table below.
Acceleration is often used to describe a state when speed increases but in Physics, acceleration is the rate of change of velocity with time. Any change in the velocity of an object results in an acceleration: increasing speed as well as decreasing speed (deceleration or retardation), or changing direction (centripetal acceleration). Acceleration is directly proportional to the sum of all forces acting on an object and inversely proportional to its mass, according to Newton's second law. It's all plain sense: if multiple different forces are pushing an object, add them up (they may be acting in opposite directions) and divide the resulting net force by the mass of the object.
According to this acceleration definition, acceleration and force are the same things. When the force varies, the acceleration changes as well, but the size of the change is determined by the object's mass. This is not the case when the mass is also changing.
Units of Force and Acceleration
The direction towards which the force is applied is called the direction of the force, and the application of force is the point where force is applied. Force can be measured by using a spring balance. The SI unit of force is Newton(N). Its dimension is LMT-2. We denote force with the letter 'F'.
Calculating acceleration is dividing velocity by time — or in terms of SI units, it is dividing the metre by seconds. Dividing distance by the time twice is the same as dividing distance by the square of time. Therefore, the SI unit of acceleration is metre per second squared (m/s2). Acceleration is denoted with 'a'.
If t (time taken), v (final velocity), and u (initial velocity) are provided. Then, the acceleration is given by the formula:
v=u+at
v²=u²−2as
\[s = ut + \frac{1}{2} at^{2}\]
Where
Final velocity is ‘v’.
Initial velocity is ‘u’.
Acceleration is ‘a’.
Time taken is ‘t’.
Distance travelled is ‘s’.
Relationship Between Force and Acceleration
The relationship between force and acceleration is shown by the equation F=ma, where “F” stands for force, “m” stands for mass, and “a” stands for acceleration. Force is a push or pull that an object exerts on other objects. Acceleration is the rate of change of the speed of an object, so if an object has mass, and it is accelerating through space, then the object is said to exert a force. This principle is described by Newton’s second law of motion.
According to Newton's first law, we know that a body will continue to be in a state of rest or uniform motion until an external force acts on it. Force can be described as an interaction that changes the state of a body that is from a state of rest to the state of motion or vice-versa. We must notice that the law says net force should act on the body. So, we will see what that actually means by considering the following situation -
(Image will be uploaded soon)
Here, one force is acting towards the right and an equal and opposite force is acting towards the left, hence, the net force on the body is zero. So, if a force is acting on a body that does not mean that the state of the body will have to change, it may or it may not. Some known forces are frictional force, gravitational force, normal force, etc.
If a net force acts on the body, then the velocity of the body either increases or decreases. Thus, this rate of change of velocity of the body is acceleration. We also observe that the greater the force, the greater wil be its acceleration. So, there has to be some relation between force and acceleration.
F = ma
Where,
F=force
m=mass
a=acceleration.
From this relation, it is understood that acceleration not only depends on the force applied to it but also on the mass of the body on which it is applied. If the same force is applied to two different bodies, then the one with a smaller mass will have greater acceleration. This was just an introduction to force and acceleration. So, the rate of change of velocity of a body is nothing but its acceleration. We also observe that the greater the force, the greater the acceleration. Hence, there must be some relation between force and acceleration. This is what is given by Newton's Second Law.
Fun Facts
Sir Isaac Newton was the first scientist to study gravity and force. His three laws are still used by scientists even today.
Force was described by Isaac Newton in his law called Newton’s second law of motion.
Any kind of force is just a push or a pull in reality.
Magnetism is a type of force. An object might be pulled by a magnet towards it or be pushed away.
Inertia is not a force.
Torque is a kind of force that rotates or twists the objects.
Gravitational and electromagnetic forces don’t need to have contact with the object for exerting force. They can exert a force on objects which are away from them.
Objects with acceleration can’t reach the infinite velocity. The fastest possible velocity is the velocity of light, which is around 299,792,458 m/s.
Acceleration is produced by the force on an object.
Negative acceleration is also known as retardation.
FAQs on Force and Acceleration
1. What is the fundamental difference between force and acceleration?
The fundamental difference is that a force is a push or pull that can cause an object to change its state of motion, while acceleration is the rate at which the object's velocity changes as a result of that force. In simple terms, force is the cause, and acceleration is the effect. An object cannot accelerate without a net force acting on it.
2. How are force, mass, and acceleration related according to Newton's Second Law of Motion?
Newton's Second Law of Motion describes a direct relationship between force, mass, and acceleration. The formula is F = m × a, where:
- F is the net force applied to the object.
- m is the mass of the object.
- a is the acceleration produced.
This means that the acceleration of an object is directly proportional to the net force applied and inversely proportional to its mass.
3. What are some real-world examples of force causing acceleration?
Understanding force and acceleration is easy with real-world examples:
- Pushing a shopping cart: The force you apply with your hands causes the cart (mass) to accelerate from a standstill.
- A car speeding up: The engine generates a force that pushes the car forward, causing it to accelerate and increase its speed.
- An apple falling from a tree: The Earth's gravitational force pulls the apple downwards, causing it to accelerate towards the ground.
- Kicking a football: The force from your foot causes the ball to rapidly accelerate into the air.
4. What happens to an object when subjected to balanced vs. unbalanced forces?
The effect depends on whether the forces are balanced or unbalanced:
- Balanced Forces: When balanced forces act on an object, the net force is zero. If the object is at rest, it remains at rest. If it is already moving, it continues to move at a constant velocity (no change in speed or direction).
- Unbalanced Forces: When an unbalanced force acts on an object, there is a net force. This net force causes the object to accelerate, meaning its speed, direction, or both will change.
5. Why does a heavier object require more force to achieve the same acceleration as a lighter one?
A heavier object requires more force because it has greater mass, which is a measure of its inertia. Inertia is an object's natural resistance to a change in its state of motion. Because a heavier object has more inertia, a greater unbalanced force is needed to overcome this resistance and make it accelerate at the same rate as a lighter object.
6. Can an object have zero acceleration even if multiple forces are acting on it? Explain how.
Yes, an object can have zero acceleration even with multiple forces acting on it. This occurs when the forces are balanced. For example, in a game of tug-of-war, if both teams pull with equal force in opposite directions, the forces cancel each other out. The net force on the rope is zero, and therefore, it does not accelerate, even though significant forces are being applied.
7. What does it mean when acceleration is negative, and what kind of force causes this?
Negative acceleration, also known as deceleration or retardation, means an object is slowing down. This is caused by a net force acting in the opposite direction to the object's motion. For example, when you apply the brakes on a bicycle, the force of friction from the brake pads acts against the wheel's motion, causing the bicycle to slow down (decelerate).
8. How is the concept of momentum connected to force?
Momentum is the product of an object's mass and velocity (p = mv). Newton's Second Law can also be stated as: the net force applied to an object is equal to the rate of change of its momentum. This means a force is what is required to change an object's momentum, either by changing its speed or its direction. A large force will cause a rapid change in momentum.
