Impulse Formula with Solved Example

Impulse formula

The impulse formula is used to calculate impulse. Impulse, usually denoted by J, refers to a great force applied for a small period of time. For instance, if a fast-moving object suddenly hits a wall, the force applied is great, but it is for a short duration of time. This force is called impulse and the formula used to calculate it is called the impulse formula. 

What does the impulse formula say? 

According to the impulse formula, if we analyze the relationship between impulse and momentum, it states that the change in momentum is always equal to the impulse of that object. Therefore J is equal to delta P. Here J represents Impulse and delta P represents momentum. 

The formula for calculating impulse: 

To calculate impulse, we have different formulas: 

1. By using force and time: We need to find the force applied on an object and the time interval. Then it is calculated by multiplying the force and that time. So, J= F*T. Here F represents force (in newton) and T represents time. 

2. By using momentum change: The formula to calculate impulse through momentum change is by calculating the mass of the body and the velocity. In this case, Impulse will be equal to the product of mass and velocity. So J= m*v. Here v will be calculated by subtracting the final velocity from the initial velocity. 

Example 1: Find out the impulse of the ball if its speed was 12 meters per second and the mass is 0.15 kg. 

Answer: Initial velocity = final velocity= 12m/s and mass= 0.15 kg. 

Using the formula, J= mv, where v= final- initial velocity. Here v= -24 and m= 0.15kg 

So J= 0.15* -(-24)= -3.6 N

Thus the impulse of the ball is 3.6 N in the negative direction. 

Example 2: If a ball of 45 grams travels at a speed of 40 meters per second, and there was a contact of three seconds between the ball and the cricket bat. What is the average impulse force applied to that ball? 

Answer: Mass= 45 gm= 0.045 kg 

Initial Velocity = 0 (because ball was at rest), final velocity= 40 m/s. Thus v= 40-0= 40 m/s. 

Now impulse force= mv= 0.045* 40. 

A further 3 seconds time period is given. Therefore impulse comes out to be 0.045* 40/3 = 600 N. 

In this way, you can calculate more such questions on the impulse formula.