Momentum and Impulse (Formulas, Example Problems, Relationships)

Bridges that are often passed by large trucks will usually be damaged more quickly than bridges that are only passed by smaller vehicles. Apparently, it is related and can be explained by the formula for momentum and impulse in physics.

Momentum and impulse are two related concepts. It is necessary to learn from understanding, the relationship between the two to the formula used to solve a problem. Check out the full explanation below.

What is Momentum?

All objects that can move must have their own momentum. In physics, the definition of momentum is a vector quantity whose direction is the same as the direction of the object's velocity.

Related to the previous statement, momentum also refers to the product of the total weight of an object and the velocity of an object. Simply put, momentum is a measure of the difficulty of making an object stop moving.

Momentum possessed by an object is influenced by two things, namely mass and velocity. If object A has a heavy mass, then its momentum is also large. Likewise with speed, the momentum of object B will increase the faster the object moves.

Let us understand by taking a simple example. Two cherries with the same weight, but located on branches of different heights, then the cherry on Tall branches will cause more pain when they fall to their feet than cherry trees on lower branches low.

Another example is when there is a collision between 2 vehicles. Vehicles that have a higher speed, of course, will experience more severe damage than other vehicles that are slower.

Read: Business Formula

What is Impulse?

In short, an impulse is a change in momentum that proves that the two concepts are indeed related. Impulse is the product of force and time as long as the force acts on an object.

In addition, impulse is defined as a vector quantity whose direction is the same as the direction of the force. This concept shows the fact that a large force is needed to move an object that was at rest or to stop an object that was moving.

The easiest example to illustrate an impulse is when a player kicks the ball in a certain direction. The moment between when you apply a force to the ball by swinging your foot until the foot finally touches the ball is called the impulse.

Read: Newton's Laws 1, 2, 3

Momentum and Impulse Formulas

How to know momentum and impulse? There is a formula used in calculating the two physics concepts.

a. Momentum Calculation

In the calculation, the following momentum formula is used:

p = m v

The formula shows momentum as a vector quantity that has a direction. That way, the direction of motion of an object can already be known if the magnitude of its momentum is found.

b. Impulse Counting

The formula for calculating impulses is as follows:

Although impulse and momentum are two related concepts, impulse still has an independent formula. That is, the formula is used when the velocity and total weight of the object are unknown.

Meanwhile, when mass and velocity are clearly known, the calculation uses a formula that states the relationship between the two concepts.

Relationship between Momentum and Impulse

Momentum and impulse have a relationship which is stated in the impulse-momentum theorem, namely the impulse acting on an object is the same as the change in momentum that occurs on the object.

The relationship between the two can be seen clearly in Newton's Second Law. The statement in Newton's Second Law emphasizes that the magnitude of the force exerted on object A will be equal to the change in momentum that occurs per unit time.

In mathematical equations, the relationship between momentum and impulse is expressed as follows:

p refers to the change in momentum ( p2 – p1)

Read: Power Dimension

Sample Questions and Discussion

An effective way to understand the momentum and impulse formulas more deeply is to practice solving problems. Here are some examples of questions about impulse and momentum along with a complete discussion:

1. A person throws a ball weighing 0.15 kg with a speed of 20 m/s. After that, the ball is hit with a stick so that it moves in a different direction with a speed of 20 m/s. Calculate the impulse given by the stick to the ball!

Based on the questions, some of the known data are:

Based on these calculations, it can be seen that the impulse is – 6 Ns.

2. Mirna rides a motorcycle with a speed of 30 m/s. The mass of the motorcycle is 200 kg. Set the momentum!

From the question, it can be seen as follows:

In this way, the momentum of Mirna's motorcycle is 6000 kg m/s.

3. Bayu is holding a ball weighing 0.5 kg. The ball begins to move with a speed of 4 m/s. After that, Ardi hit the ball by giving the opposite force so that the speed of the ball changed to 8 m/s. If the ball hits the bat for 0.01 seconds, then calculate how much change in momentum occurs!

Based on the question, it is known:

In the problem, the thing that is being asked is the change in momentum which means the same as the impulse. Then the calculation becomes:

So, the change in impulse or momentum of the ball is – 6 m/s.

4. A large truck weighing 2 tons is driven at a speed of 72 km/hour. While turning at a fork, the truck hit a pole and stopped moving for 0.1 second. What is the average force (F) on the truck at the time of the collision?

From the question, it can be seen:

Now, you understand about momentum and impulse, right? The momentum formula is used to find out how much momentum a moving object has. The change in momentum of an object is equal to the impulse on that object.