Impulse
Impulse definition: Impulse means the amount of change that happens to an object’s momentum when a force is applied to it for a period of time. Momentum is how much motion an object has. For example, when you kick a football, your foot pushes the ball with a force for a short time. That push changes the ball’s momentum. This whole action is called impulse.
Vector property: Impulse is a type of quantity that has both magnitude and direction. This means we not only care about how much impulse there is (the size), but also which way it is acting. The direction of impulse is the same as the direction of the force that caused it.
Formula: The formula for impulse is written as J = F × t. Here, J stands for impulse, F is the size of the force, and t is how long the force is applied. This means if a big force acts for a long time, the impulse will be large.
Link to momentum: We can also understand impulse by looking at the formula F = Δp / t, where Δp is the change in momentum. If we rearrange this formula, we get Ft = Δp. This shows that impulse is equal to the change in momentum.
Expanded form: If we know an object’s mass (m), its final velocity (v), and its initial velocity (u), we can write impulse as J = mv – mu. This formula gives us a clear way to calculate how much momentum has changed, which is the impulse.
Effect of impulse: The more impulse you apply to an object, the bigger the change in its motion. For example, pushing a shopping cart gently changes its motion a little, but pushing it hard changes its motion a lot. Both force size and time affect how big the impulse is.
Calculations: If you know two of the three things (impulse, force, or time), you can find the third. For example, if you know the impulse and how long the force acted, you can find the force that was applied.
Units of Impulse
Standard unit: The standard unit used to measure impulse is called the Newton-second (N s). This tells us how much force was applied and how long it lasted.
Alternative unit: You might also see impulse written in kilogram metre per second (kg·m/s). This is because impulse is also equal to the change in momentum, which is measured in these units.
Unit equivalence: These units are actually the same. A Newton is equal to 1 kg·m/s². When we multiply by time (seconds), we get 1 N s = 1 kg·m/s.
Impulsive Force
Definition: Impulsive force is a very strong force that acts over a very short time. It often happens during fast events like car crashes, hitting a baseball, or hammering a nail.
Formula: The formula for impulsive force is F = Δp / t or F = (mv – mu) / t. It shows that the size of the force depends on how fast the momentum of an object changes. The quicker the change, the larger the force.
Magnitude: If the momentum changes in a very short time, the force will be very large. That’s why crashing into a wall feels painful—the stop is quick, so the force is big.
Inversely related: The shorter the time of impact, the greater the force will be. This is why we use soft surfaces or padding to make impacts last longer and reduce the force.
Vector nature: Impulsive force also has both size and direction, just like impulse. It acts in the same direction as the motion change.
Units of Impulsive Force
SI unit: The unit used to measure impulsive force is called the Newton (N). This is the same unit we use for measuring all types of force in physics. It tells us how strong a push or pull is.
Alternative expression: One Newton (1 N) is equal to 1 kilogram metre per second squared (1 kg·m/s²). This means that if we apply a force of 1 N to a 1 kg object, it will speed up by 1 metre per second every second. In other words, it will keep gaining speed steadily as long as the force is applied.
Applications of Impulse and Impulsive Force
Airbags: Airbags in cars open very quickly when there is a crash. They give your body more time to slow down instead of stopping suddenly. By increasing the time, the force your body feels becomes smaller, which helps prevent serious injuries.
Crumple zones: The front and back areas of a car are designed to bend and collapse during a crash. This crumpling takes more time to bring the car to a stop, which lowers the force acting on the people inside, making it safer.
Seatbelts: During a crash, seatbelts stretch a little bit instead of stopping you suddenly. This extra stretching time helps reduce the force acting on your body, keeping you safer.
Catching a ball: When you catch a fast-moving ball, if you move your hands backward while catching it, you give the ball more time to stop. This makes the force on your hands smaller and prevents pain or injury.
Hitting a ball: When a bat hits a ball quickly, the time of contact is very short. Because the time is short, the force becomes large, which helps the ball fly far.
Boxing gloves: Gloves used in boxing have thick padding. This padding spreads the impact over a longer time, which lowers the force and makes it safer for both the person punching and the person getting punched.
Landing in jumps: Athletes bend their knees when landing from a jump. This action increases the time it takes for them to stop, which lowers the force on their legs and prevents injury.
Protective packaging: Fragile items are often packed with bubble wrap or foam. These materials increase the time it takes for the object to come to a stop if dropped, reducing the force and preventing breakage.
Pile drivers: A pile driver is a machine that drops heavy weights onto posts to push them into the ground. Because the weight hits in a very short time and has a lot of mass, the force is very big and effective.
Pestle and mortar: When we crush things like spices or medicine using a pestle and mortar, we use quick and hard hits. The short time of impact creates large forces that help break the materials.
Hammering: When we use a hammer to drive a nail, we swing it quickly to hit the nail hard in a short time. This creates a big force that pushes the nail into the material easily.
Padded dashboards: In some cars, the dashboard is made with soft padding. If a person hits it in a crash, the padding helps spread out the impact time, reducing the force and chances of injury.
Mattresses: When someone falls onto a mattress, the soft surface takes longer to stop the person. This longer stopping time means the force on the body is smaller, making the landing safer and more comfortable.
Relationship Between Impulse and Impulsive Force
Impulse as force-time product: The formula J = Ft means that impulse (J) is equal to the force (F) multiplied by the time (t) that the force acts. This tells us that both how strong the force is and how long it lasts matter when it comes to changing an object’s motion.
Impulsive force as rate: Impulsive force describes how quickly an object’s momentum changes. If the change in momentum happens very fast, the force involved will be large. The faster the change, the stronger the force.
Direct link: Impulse is always equal to the change in momentum. That means when a force acts on something and changes how fast it’s moving, we call that change an impulse.
Time effect: If you make the object stop over a longer period of time, the force needed is smaller. That’s why soft landings and padding help reduce injuries—they give more time for the object to stop and lower the force felt.
Key Points to Remember
Impulse definition: Impulse is the total change in an object’s momentum that happens when a force is applied for a certain amount of time.
Impulse formula: The formula is J = Ft, where J stands for impulse, F is the force, and t is the time the force acts.
Impulsive force: This is a strong and quick force that happens during fast events, like a punch or a crash.
Impulse units: Impulse can be measured in Newton-seconds (N·s) or in kilogram metres per second (kg·m/s). Both units mean the same thing.
Force units: Force is measured in Newtons (N), and 1 Newton is equal to 1 kg·m/s².
Inverse relationship: If the time is very short, the force becomes bigger. If the time is longer, the force becomes smaller. This is why we try to increase stopping time to reduce the force.
Practical importance: Understanding how impulse and impulsive force work helps engineers and scientists make things safer. They can design better cars, helmets, sports gear, and packaging to protect people and objects. Athletes can also use this knowledge to perform better and avoid injuries