Momentum and impulse are fundamental concepts in physics, offering insights into the motion of objects and their interactions. This guide will break down these concepts, provide problem-solving strategies, and highlight their real-world applications.
Momentum: The Measure of Motion
What is Momentum?
Momentum (“p”) measures an object’s motion and resistance to changes in velocity. It is defined as the product of an object’s mass (“m”) and velocity (“v”):
Units: Momentum is measured in .
Vector Quantity: Momentum has both magnitude and direction. The direction is the same as the object’s velocity.
Key Points to Remember:
Momentum depends on the mass and velocity of an object.
A system’s total momentum is the vector sum of the momenta of all objects in the system.
The law of conservation of momentum states that in a closed system with no external forces, total momentum remains constant.
Example Problem 1: Calculating Momentum
Problem: A ball of mass 0.2 kg is thrown with a velocity of 20 m/s. What is its momentum?
Solution:
Answer: The momentum of the ball is .
Impulse: Changing Momentum
What is Impulse?
Impulse (“J”) measures the change in an object’s momentum due to a force applied over a period of time:
Units: Impulse is measured in or , the same as momentum.
Vector Quantity: The direction of impulse matches the applied force’s direction.
The Momentum-Impulse Theorem
The theorem states:
This means impulse equals the change in momentum.
Example Problem 2: Calculating Impulse
Problem: A bowling ball of mass 6 kg rolls at 10 m/s and collides with pins, coming to rest after 0.2 seconds. What is the impulse during the collision?
Solution:
Initial momentum: .
Final momentum: .
Change in momentum: .
Answer: The impulse is .
Real-World Applications
Car Safety Features: Airbags increase the collision time (∆t), reducing the force (∆p = F∆t) experienced by passengers.
Sports: Athletes use follow-through techniques to maximize the time of impact, increasing the momentum transfer to the ball.
Rocket Thrust: Rockets expel fuel, generating thrust via changes in momentum (∆m/∆t).
Key Problem Types
Conservation of Momentum
This principle applies in collisions and explosions.
Example Problem 3: Collision
Problem: A 2000 kg car moving at 10 m/s collides with a stationary 3000 kg truck. After the collision, they stick together and move at the same velocity. What is their final velocity?
Solution:
Total initial momentum: .
Combined mass: .
Final velocity: .
Answer: The final velocity is .
Force vs. Time Graphs
The area under a force-time graph represents impulse.
Example Problem 4: Impulse from a Graph
Problem: A force-time graph shows a triangular shape with a peak force of 300 N and a time of 0.2 s. What is the impulse?
Solution:
Area of triangle: .
.
Answer: The impulse is .
5.2 Representations of Changes in Momentum
5.2 Representations of Changes in Momentum