What Is the Difference Between Force and Momentum?
Confused between the two terms, momentum and force? Here, you will learn the relation between force and momentum and the crucial points of difference between them. Generally, momentum refers to the quantity that tells about the content motion present in any moving object. However, force refers to the amount that changes the amount of action present when acted upon any object.
The amount of motion encompassed within a moving object refers to momentum. It is a vector quantity whose direction depends on the velocity direction. Unlike force, there is no such classification of momentum. So, what is momentum? An unbalanced force acting upon an object always results in momentum.
Mass times velocity of any object stands as momentum.
It generally doubles when the velocity gets increased.
Additionally, if the two objects are moving with the same velocity, but having different masses, the momentum will be large for the object having a large mass.
Kgm/s is the unit to define momentum.
What is a Force?
A force refers to the external action of pushing or pulling something, which results in the momentum change. It is a vector quantity whose direction depends on the acceleration direction. An unbalanced force applied to the body results in the movement of that object. However, the force acting in a balanced way results in equal magnitude but opposite direction. As a result, the net effect cancels out.
That is why; an object does not move in case of the balanced force applied, and hence the velocity remains zero. It implies that momentum will also be zero as momentum = mass * velocity.
Forces can be categorized into two major types:
Contact Forces– These are the forces that result from the actual contact between two objects. For instance, a bat hitting a ball is a practical example of contact forces.
Forces Acting at a Distance– Without any physical contact, the forces acting between the objects are defined under this category.
Moreover, the force can be categorized in numerous ways, depending on classification. For instance, in terms of work, if the job done is positive, then it implies force acting in a positive direction, and if the work done is negative, then it means that the object is moving in the opposite direction of the work done. Hence, the force acting is negative in this case. Mathematically, mass into acceleration (ma) refers to force, whereas momentum refers to mass into the velocity of an object.
In the picture above, you will find that motion, force, and momentum have a correlation with each other. If you apply a force, an object in rest will start moving and generate momentum. However, momentum is the product of mass and velocity.
How can You Change an Object’s Momentum to its Force?
Force and momentum relation is given by the equation:
F=dp/dt. The second law of motion gives the following equation as stated by Newton. The law states that the change in momentum of any object is given by mass into acceleration, that is, force.
From the above equation, if the mass is constant, then, p=mv implies dp = mdv.
Hence, the equation becomes F = m * dv/dt, which is equal to ma.
Force and momentum relation can also be stated through the following equations:
Momentum= (mass * velocity)
As acceleration = velocity/time implies velocity = acceleration * time
So, momentum= (mass * (acceleration * time))
momentum = ((mass * acceleration) * time)
momentum = force * time
From the above equation, it is clear that momentum depends on time. It shows that as large a force is practiced on an object, the amount of momentum will increase. However, the force does not depend on the time in the same way as momentum. It means that with the increasing time, there will be a decrease in the amount of force if the momentum remains constant.
Momentum and force both have magnitude as well as direction. It means both are vector quantities.
If the velocity changes, then from the formula; p = mv;, momentum also changes. However, force changes only when the acceleration changes. Even if there is a change in the velocity of an object, but acceleration remains constant, then the force will also remain constant.
Difference Between Force and Momentum
FAQs on Force and Momentum Explained: Physics Fundamentals
1. What is the fundamental concept of momentum in physics?
Momentum is a measure of an object's motion, often described as 'mass in motion.' It is a vector quantity, meaning it has both magnitude and direction. Quantitatively, it is the product of an object's mass (m) and its velocity (v). The formula is expressed as p = mv. An object must be moving to have momentum; a stationary object has zero momentum.
2. How are force and momentum fundamentally related according to Newton's Second Law?
The fundamental relationship is that force is the rate of change of momentum. According to Newton's Second Law of Motion, the net force applied to an object is equal to the change in its momentum over time. This is mathematically written as F = Δp / Δt. This means a force must be applied to change an object's momentum, either by altering its speed, its direction of motion, or both.
3. What is the main difference between force and momentum?
The main difference lies in what they describe and how they function:
- Momentum (p) is an intrinsic property of a moving object, calculated as mass times velocity (p = mv). It quantifies the amount of motion an object has.
- Force (F) is an external influence, like a push or a pull, that causes a change in an object's momentum. It is not something an object possesses, but something that acts upon it.
4. What is impulse, and how does it connect force to a change in momentum?
Impulse is the product of the force applied to an object and the time interval over which that force acts (Impulse = F × Δt). The Impulse-Momentum Theorem states that the impulse applied to an object is precisely equal to the change in its momentum (Δp). This is a crucial concept in real-world applications. For instance, airbags in cars increase the collision time (Δt), which reduces the peak force (F) on a passenger for the same change in momentum, thereby minimising injury.
5. Why is the principle of conservation of momentum considered a fundamental law of physics?
The principle of conservation of momentum is fundamental because it holds true for any isolated system—one where no external forces are acting. It states that the total momentum of all objects within that system remains constant before, during, and after any interaction, such as a collision. This law is universally applicable and essential for analysing:
- Collisions between any objects (from subatomic particles to galaxies).
- Explosions and recoil actions (like a cannon firing a ball).
- The propulsion of rockets and jet engines.
6. How does a rocket apply the principle of conservation of momentum to travel in the vacuum of space?
A rocket operates by creating an isolated system consisting of the rocket and its fuel. To move, it expels hot gases from its engines at extremely high velocity. Before launch, the total momentum of the rocket-fuel system is zero. When the rocket ejects gas backwards, this gas gains a large momentum in the backward direction. To keep the total momentum of the system conserved (i.e., at zero), the rocket must gain an equal amount of momentum in the forward direction. This forward momentum causes the rocket to accelerate, allowing it to travel in space where there is no air to push against.
7. Can a system of objects have zero total momentum but still have kinetic energy?
Yes, this is an important distinction between momentum and energy. A system can have zero total momentum while having non-zero total kinetic energy. Consider a simple example: two identical billiard balls moving towards each other at the same speed.
- Momentum: As momentum is a vector, their momentums are equal in magnitude but opposite in direction (e.g., +p and -p). The total momentum of the system is (+p) + (-p) = 0.
- Kinetic Energy: As kinetic energy (KE = ½mv²) is a scalar and always positive, the total kinetic energy is the sum of their individual energies, which is a positive value.
