# Impulse – Definition, Formula, Applications

A person can use impulse on a regular basis or once in a while. It is also the principle that we employ anytime we strike a ball. In addition, we will cover impulse, the impulse formula, the derivation of the impulse formula, and a solved case in this field. We’ll also learn about the relationship between momentum and impulse.

We have kicked a ball, punched a punching bag, and participated in sports using any type of ball in our daily lives; in all of these activities, we employ impulse without realizing it. As a result, what is impulse, and what does it have to do with these situations? We must first discuss the idea of momentum before we can consider impulse.

### Momentum

The term “momentum” relates to the strength of something. It also serves as a gauge for how difficult it is to bring an item to a halt.

Furthermore, a stable or motionless object has no or zero motion. Moreover, a huge, slow-moving item has significant momentum, as does a tiny, fast-moving item. A force can influence an object’s velocity in either direction. In addition, if the object’s velocity varies, the momentum changes as well.

In athletics, the term “momentum” is frequently used. When a pundit states that a player has momentum, it signifies that the person is genuinely moving and that stopping him or her is extremely tough. Because a body with momentum cannot be halted, it is necessary to exert a force against its direction of motion for a certain amount of time. The more momentum there is, the more it is difficult to halt. As a result, a greater amount of power is necessary, as well as a significant length of time to bring the body to a complete stop. The body’s velocity varies as force works on it for a specific period of time, and therefore the body’s momentum changes.

**Momentum Formula**

The formula for the momentum of any object is given as:

p = mvwhere,

- m is the mass of object
- p is the momentum
- v is the velocity of object.

Furthermore, momentum is a vector that equals the product of velocity vector and mass. But what is the relationship between impulse and momentum? When a force operates on an item for a brief period of time, the measure of how much the force modifies the item’s momentum is called impulse.

### Impulse and its Equation

When a net force acts on a body, it causes acceleration, which changes the body’s motion. A larger net force will result in a greater acceleration than a small net force. If the big and tiny forces occur at different time periods, the overall change in motion of the item might be the same. The combination of force and time that it acts is a valuable quantity that leads to the definition of impulse.

The product of the average net force acting on an item for a certain period of time is sometimes referred to as the impulse.

**The following is the formula for impulse:**

J = F × ΔtHere,

- J is the impulse
- Δt is the time interval
- F is the force.

It’s worth noting that we assume force remains constant throughout time. Like force, the impulse is a vector quantity with a direction.

### Impulse-Momentum Theorem

A person must know the mechanics of collisions. The laws of momentum and first law (known as the change in impulse equation) govern collisions. In a collision, the body is subjected to a force for a specific amount of time, resulting in a change in momentum. The body either slows down, speeds up, or changes direction as a result of a force acting for a certain length of time.

In a collision, the item receives an impulse that is equivalent to a change in momentum. Consider a footballer who is sprinting down the field when he collides with a defensive back. The halfback’s pace and momentum change as a result of the contact.

The Impulse-Momentum theorem aids in the understanding of these two concepts. The theorem simply asserts that the change in an object’s momentum is proportional to the amount of impulse applied to it.

The alternate formula of impulse is given as:

J = Δp = p_{f }− p_{i}where,

- Δp is the change in momentum
- p
_{f}is the final momentum- p
_{i}is the initial momentumSince, mass of the object remains constant, it can also be given as:

J = m × (v_{f}−v_{i})where,

- m is mass of the object
- v
_{f}is the final velocity- v
_{i}is the initial velocity

Most importantly, the formula correlates impulse to the object’s change in momentum. In addition, impulse can be measured in kilogram meters per second (kg m/s) or Newton times seconds (Ns).

### Impulse Examples

A few of the examples of impulse is given below:

- When someone falls from a bed onto a floor, they sustain more damage than if they fall onto a heap of sand. This occurs because the sand yields more than the cemented floor, increasing the contact time and reducing the force effect.
- For the same reason, nylon ropes are utilized in the sport of rock climbing. Climbers use nylon ropes to secure themselves to the rock faces. A rock climber will start to tumble if she loses her grasp on the rock. In this case, her speed will be eventually slowed by the rope, averting a dangerous fall to the ground below.
- Hitters are frequently instructed to follow through while striking a ball in racket and bat sports. High-speed videos of the collisions between bats/rackets and balls have indicated that the act of following through serves to lengthen the duration over which a collision occurs. In the impulse-momentum change theorem, this increase in time must result in a change in another variable.

### Sample Problems

**Problem 1: An item comes to a halt when it collides with a solid wall. Calculate the object’s impulse if the object was 2.0 kg in weight and traveled at a speed of 10 m/s before colliding with the wall.**

**Solution:**

Given:

Mass of the object, m = 2.0 kg

Initial velocity of the ball, v

_{i }= 10 m/sFinal velocity of the ball, v

_{f }= 0 m/sThe formula for impulse is:

J = m × (v

_{f}− v_{i})Substitute all the values in the above equation.

J = 2 × (0 – 10) kg m/s

= -20 kg m/s

Hence, the impulse on the object is

-20 kg m/s.

**Problem 2: A golfer hits a ball of mass 100 g at a speed of 50 m/s. The golf club is in contact with the ball for 2 ms. Compute the average force applied by the club on the ball?**

**Solution:**

Given:

Change in the velocity, Δv = 50 m/s

Mass of the ball, m = 100 g = 0.1 kg

Time of contact, t = 2 ms = 0.002 s

The formula of impulse is:

J = F × Δt = m × Δv

F = m × Δv / Δt

Substitute all the values in the above equation.

F = (0.1) × (50) / 0.002 N

=2500 N

Hence, the average force applied on the ball is

2500 N.

**Problem 3: Which two laws govern the collisions?**

**Answer:**

The laws of momentum and Newton’s first law governs collisions. These laws together gives the impulse equation which simply asserts that the change in an object’s momentum is proportional to the amount of impulse applied to it.

**Problem 4: Why a person gets more injury falling onto a floor rather than on sand?**

**Answer:**

When someone falls from a bed onto a floor, they sustain more damage than if they fall onto a heap of sand. This occurs because the sand yields more than the cemented floor, increasing the contact time and reducing the force effect.

**Problem 5: Calculate the impulse on a body hit by a force of 500 N with a time of contact equal to 0.1 s.**

**Solution:**

Given:

The force exerted on body, F = 500 N

Time of contact, Δt = 0.1 s

The formula for impulse is:

J = F × Δt

=(500) × (0.1) N s

= 50 N s

Hence, the impulse on body is

50 N s.