Force and Momentum

What is Force?

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 contented 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 a 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 the 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 mass, the momentum will be large for the object having 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 acted 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 Namely; 

  • 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 based on classification. For instance, in terms of work, if the job done is positive, then it implies force acting is in a positive direction, and if the work is 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. 

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In the picture above you will find that motion, force, and momentum has a correlation with each other. If you apply a force, an object in rest will start moving and generates 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 practised 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. The key points of differences between force and momentum:

Difference Between Force and Momentum

Force

Momentum

Force = mass * acceleration or f=ma

Momentum = mass * velocity or p=mv

For the stationary object, the forces can exist.

The momentum for the stationary objects is always zero.

The direction of the force depends on the acceleration.

The direction of the momentum rests on the direction of the velocity.

The force is inversely proportional to time, that is; with the increase in time, the force decreases.

The momentum is directly proportional to time; that is; with the increase in time, the momentum also increases.

For constant acceleration, this quantity does not change.

The momentum changes for the constant acceleration, but remains constant if the velocity is constant.

FAQ (Frequently Asked Questions)

1. How Force Relates to Momentum?

If you know the amount of force to apply, you change its momentum with the applied force. Force defines the rate with which momentum of an object changes. Momentum is all about the motion of an object. If an object moves with a double velocity, his momentum doubles, Force cause the change in momentum of the object as you change its speed. So, momentum is the multiple of force and time. But if you keep applying force for a particular time, it will change its momentum. It follows the third law of motion by Newton. 

2. How you use Momentum? Give a Real-time Example.

In real-life, suppose we drive a vehicle at high speed. Fast running cars will have high momentum, and when they get hit, it causes a lot of damage, and we get injured. Our vehicle collides due to a sudden change in velocity and, thus, the applied force. Although your car is small, it has massive momentum due to high velocity. Every activity that brings motion is us momentum is associated with it. Now suppose, if you throw a cricket ball with different speed, it will have different momentum. Hence the momentum of two objects with the same mass is all dependent upon the velocity.