Change in Momentum Calculator

How to Find Change in Momentum?

In the context of physics, the change in momentum is the difference between the final momentum and the initial momentum of an object. Momentum itself is defined as the product of an object's mass and its velocity. Understanding the change in momentum is fundamental in analyzing collisions, explosions, and any scenario where forces act on an object over time. This concept is intimately linked to impulse, which is the total effect of a force acting over a period.

The momentum of an object changes due to its velocity. The formula for change in momentum is given by:

\[ \Delta p = m \, \Delta v \]

The momentum change formula can be elaborated in more detail as:

\[ \Delta p = p_2 - p_1 = m v_2 - m v_1 = m \, \Delta v \]

Here, \(\Delta p\) represents the change in momentum over a particular period of time. To calculate the change in momentum, subtract the final momentum \(p_2\) from the initial momentum \(p_1\), which occurs due to the change in velocity. The final momentum calculator will identify the change in momentum of an object with respect to its velocity shift.

What is Impulse?

The change in momentum is known to be the impulse and it is represented as the “J”. The formula for calculating change in momentum or impulse is given by:

The impulse of an object is given by:

\[ J = F \, t \]

Impulse is also equal to the change in momentum:

\[ J = \Delta p \]

The units of impulse or momentum are "Ns" or "kg·m/s". If you are finding the impulse or the change of momentum, you can check your answers using the impulse and momentum calculator. Both terms have the same meaning and purpose in physics.

Example:

Calculate the change in momentum of an object of mass \(100 \ \text{kg}\), uniformly accelerated from an initial velocity of \(5 \ \text{m/s}\) to \(8 \ \text{m/s}\) over a period of \(6 \ \text{s}\).

Given:

• Initial velocity: \(u = 5 \ \text{m/s}\)
• Final velocity: \(v = 8 \ \text{m/s}\)
• Mass: \(m = 100 \ \text{kg}\)
• Time: \(t = 6 \ \text{s}\)

Solution:

Step 1: Initial momentum:

\[ p_1 = m u = 100 \times 5 = 500 \ \text{kg·m/s} \]

Step 2: Final momentum:

\[ p_2 = m v = 100 \times 8 = 800 \ \text{kg·m/s} \]

Step 3: Change in momentum (Impulse):

\[ \Delta p = p_2 - p_1 = m v - m u = m \Delta v \] \[ \Delta p = 800 - 500 = 300 \ \text{kg·m/s} \]

The change in momentum is also known as the impulse of a moving object. You can calculate it using the impulse and momentum calculator.

Step 4: Find the force acting on the object:

\[ F = \frac{m(v-u)}{t} = \frac{p_2 - p_1}{t} = \frac{300}{6} = 50 \ \text{N} \]

The following results are obtained:

Initial momentum: \[ p_1 = m u = 500 \ \text{kg·m/s} \]

Final momentum: \[ p_2 = m v = 800 \ \text{kg·m/s} \]

Magnitude of the force: \[ F = 50 \ \text{N} \]

The total momentum calculator finds both the momentum and the applied force on the object.

How to Find Momentum with Force and Time?

According to Newton’s second law of motion, force is equal to the product of mass and acceleration:

\[ F = m a \]

Acceleration is the change in velocity with respect to time:

\[ a = \frac{\Delta v}{t} \]

Substitute \(a\) into the force equation:

\[ F = m \frac{\Delta v}{t} = \frac{m \Delta v}{t} \]

Since the change in momentum is:

\[ \Delta p = m \Delta v \]

We can rewrite the force formula in terms of momentum:

\[ F = \frac{\Delta p}{t} \]

Rearranging this gives the change in momentum in terms of force and time:

\[ \Delta p = F \, t \]

The change in momentum and the applied force are directly proportional to each other. Our momentum calculator allows you to compute momentum changes by using parameters defined in Newton’s second law of motion.

Working of Change in Momentum Calculator:

Let’s have a look at the working of the total momentum calculator:

Input:

• Select the desired measurements from the list
• Enter the mass, initial velocity, and final velocity 
• Tap the calculate button

Output:

• Initial momentum 
• Final momentum 
• Change in momentum

References:

From the source of Wikipedia: How to solve for momentum, How to calculate change in momentum? From the source of the openstax.org: Momentum change formula, How to find the change in momentum?