Impulse SI Units, Dimensional Formula, and Common Exam Questions
Impulse is a fundamental concept in physics, especially in mechanics. It describes the total effect of a force acting over a period of time. This topic is crucial for understanding changes in momentum during collisions, sports actions, and many daily life events involving forces applied for short durations. Mastering impulse helps in solving advanced and competitive physics problems efficiently.
What is Impulse?
Impulse is defined as the product of force and the time interval during which the force acts on an object. It quantifies the change produced in the momentum of an object when a force is applied for a finite period. Impulse is represented by the letter J in formulas.
The mathematical equation for impulse is:
Unit of Impulse
To determine the unit of impulse, it is important to analyze the units of force and time:
- The SI unit of force is Newton (N). 1 Newton is defined as 1 kg·m/s2.
- The SI unit of time is second (s).
Combining the two, the unit of impulse becomes:
Therefore, the unit of impulse is Newton-second (N·s), which is dimensionally equal to kg·m/s (kilogram meter per second).
Impulse and Momentum – The Connection
Impulse is directly related to momentum. The change in momentum of an object is equal to the impulse given to it. This relationship is expressed as:
Here, m is mass, vf is final velocity, and vi is initial velocity. This helps solve many problems involving collisions or sudden force applications.
Step-by-Step: Deriving the SI Unit of Impulse
- Write the formula: Impulse = Force × Time (J = F × Δt)
- Substitute the SI units: Force (Newton) × Time (second)
- 1 N = 1 kg·m/s2
- Therefore, Impulse = (kg·m/s2) × s = kg·m/s
- So, both N·s and kg·m/s are valid units for impulse. Both represent the same quantity dimensionally.
| Physical Quantity | Symbol | SI Unit | Derived Unit Expression | Dimension |
|---|---|---|---|---|
| Impulse | J | N·s or kg·m/s | kg·m/s | M1L1T-1 |
| Momentum | p | kg·m/s | kg·m/s | M1L1T-1 |
Solved Example
| Problem Statement | Stepwise Solution | Answer |
|---|---|---|
| A force of 6 N is applied to a cart for 2 seconds. What is the impulse delivered? |
Impulse, J = F × Δt
= 6 N × 2 s = 12 N·s Therefore, the impulse is also 12 kg·m/s. |
12 N·s or 12 kg·m/s |
How to Identify Physical Quantities with the Same Unit as Impulse
Impulse and momentum both have the unit kg·m/s. This is because both represent a product involving mass and velocity, or force and time, which are dimensionally equivalent. When comparing, always look for quantities with the formula structure: mass × velocity.
| Physical Quantity | Formula | SI Unit |
|---|---|---|
| Impulse | F × Δt | N·s / kg·m/s |
| Momentum | m × v | kg·m/s |
Applications and Related Concepts
- Impulse answers many practical questions such as how long a force must act to stop a moving vehicle, or how much "kick" a force delivers in a short time.
- Devices like airbags in cars use the concept of impulse to reduce injury by increasing the time over which force is applied.
- Explosions, crashes, and ball games use impulse calculations to predict outcomes and ensure safety.
Practice Question
A ball of mass 0.5 kg moves with a velocity of 10 m/s and is brought to rest by a force acting for 0.2 s. What is the average force applied?
Approach to Solving Impulse-Based Problems
- Identify if the problem involves force acting over time or a sudden change in velocity.
- Use the relevant formula: J = F × Δt or J = m × Δv.
- Insert appropriate units and solve step-by-step.
- Write the final answer in correct SI units: N·s or kg·m/s.
| Key Formula | Description | Unit |
|---|---|---|
| J = F × Δt | Impulse as force multiplied by time interval | N·s |
| J = m × Δv | Impulse as change in an object's momentum | kg·m/s |
Further Learning and Next Steps
- Impulse-Momentum Theorem
- Force, Work, and Energy
- Force and Momentum
- Review Work and Power for related problems and practice questions.
Summary
Impulse helps describe the overall effect of a force acting for a certain time. Its SI unit is Newton-second (N·s), which is dimensionally the same as kilogram meter per second (kg·m/s), the unit for momentum. Understanding these units and their relationships is key for confidently solving mechanics questions, especially those involving sudden forces or collisions.
FAQs on Impulse Units in Physics: Complete Guide for JEE, NEET & Boards
1. What is the SI unit of impulse?
The SI unit of impulse is the Newton-second (N·s), which is also dimensionally equivalent to kilogram meter per second (kg·m/s). Both units are correct because impulse equals the change in momentum. This unit matches the standard set in the latest Physics syllabus for major exams.
2. How do you derive the unit of impulse in Physics?
The unit of impulse is derived as follows:
• Impulse (J) is the product of force (F) and time interval (Δt): J = F × Δt
• The SI unit of force is Newton (N) and time is seconds (s)
• Therefore, SI unit: N·s
• Since 1 N = 1 kg·m/s², the unit can also be written as kg·m/s.
This shows impulse shares its unit with momentum.
3. Is joule (J) the unit of impulse?
No, joule (J) is not the unit of impulse. Joule is the SI unit of energy. Impulse is measured in newton-second (N·s) or kg·m/s, not joule, because impulse represents a change in momentum, not energy.
4. Why is impulse measured in N·s?
Impulse is measured in N·s because it equals force (in Newtons) multiplied by time (in seconds). Since force applied over time causes a change in momentum, N·s directly reflects the physical meaning of impulse in equations.
5. What is the dimensional formula of impulse?
The dimensional formula of impulse is [M1L1T-1].
• M stands for mass, L for length, and T for time.
• This is identical to the dimensional formula for momentum.
• It confirms that impulse and momentum are closely related physical quantities.
6. What is the difference between the units of impulse and momentum?
Impulse and momentum share the same SI unit: kg·m/s or N·s. The key difference is:
• Impulse refers to the total effect of a force acting over a specific time interval.
• Momentum is the product of mass and velocity.
While their units are the same, their physical meanings and applications differ.
7. What are the CGS and Imperial units of impulse?
In different systems:
• CGS unit: dyne-second (dyn·s)
• Imperial unit: pound-second (lb·s)
These units reflect local conventions but are used less commonly than SI units in academic contexts.
8. What is the impulse-momentum theorem and its unit significance?
The impulse-momentum theorem states:
• Impulse (J) delivered to a body equals its change in momentum (Δp): J = Δp
• Units for both: N·s or kg·m/s
This theorem is crucial for solving collision and impact problems in exams.
9. Can impulse ever be negative?
Yes, impulse can be negative. The sign of impulse depends on the direction of force or change in momentum. A negative impulse indicates a force opposite to the initial motion or direction of momentum.
10. Which physical quantities have the same unit as impulse?
Momentum has the same SI unit as impulse:
• Both use N·s or kg·m/s
• Other vector quantities like linear momentum share this dimension and unit in mechanics.
This simplifies calculations involving changes in motion.
11. How do you calculate impulse if the force is not constant?
If force varies with time, impulse is found by integrating force over the time interval:
• J = ∫ F(t) dt
This calculates the total impulse delivered even for variable or non-uniform forces.
12. Why is impulse denoted by the letter ‘J’?
Impulse is represented by the symbol ‘J’ to avoid confusion with cymbols like ‘I’ (used for current) or ‘p’ (used for momentum). Using ‘J’ helps distinguish impulse clearly in equations and problems.
