This worksheet reinforces your understanding of the conservation of momentum principle. Remember, in a closed system (no external forces acting), the total momentum before a collision or explosion equals the total momentum after. We'll explore this concept through various scenarios.
What is Momentum?
Before we dive into the problems, let's review the definition of momentum. Momentum (p) is a vector quantity, meaning it has both magnitude and direction, calculated as:
p = mv
Where:
- p represents momentum (kg⋅m/s)
- m represents mass (kg)
- v represents velocity (m/s)
Practice Problems: Conservation of Momentum
Instructions: For each problem, identify the system, determine if it's a closed system, and apply the principle of conservation of momentum to solve. Show your work clearly, including diagrams where helpful.
Problem 1: The Collision
A 2 kg cart moving at 3 m/s to the right collides with a stationary 1 kg cart. After the collision, the 2 kg cart moves at 1 m/s to the right. What is the velocity of the 1 kg cart after the collision?
Problem 2: The Explosion
A 5 kg firework initially at rest explodes into two pieces. One piece, with a mass of 2 kg, moves to the left at 10 m/s. What is the velocity of the other piece?
Problem 3: Inelastic Collision
A 0.5 kg ball traveling at 4 m/s to the right collides with a 0.5 kg ball at rest. The two balls stick together after the collision. What is their final velocity? (Remember: This is an inelastic collision, meaning kinetic energy is not conserved.)
Problem 4: Two-Dimensional Collision
A 3 kg object moving at 4 m/s in the positive x-direction collides with a 2 kg object moving at 6 m/s in the positive y-direction. After the collision, the 3 kg object moves at 2 m/s at an angle of 30° above the positive x-axis. What is the velocity (magnitude and direction) of the 2 kg object after the collision? (Hint: This problem requires vector addition and resolution.)
Problem 5: Real-World Application
Explain how the principle of conservation of momentum applies to a rocket launching into space. Consider the expulsion of gases as a crucial factor.
Answer Key (For Instructor Use)
(Note: The following solutions are provided for instructors to check student work. Students should be encouraged to attempt the problems independently before consulting the answer key.)
Problem 1: The final velocity of the 1 kg cart is 4 m/s to the right.
Problem 2: The other piece moves to the right at 6.67 m/s.
Problem 3: The final velocity of the combined balls is 2 m/s to the right.
Problem 4: This problem requires vector decomposition and subsequent calculations using conservation of momentum in both the x and y directions. The final answer will involve both magnitude and direction of the velocity. (Detailed solution should be provided by the instructor.)
Problem 5: The expulsion of gases from the rocket engine exerts a force on the gases. By Newton's Third Law, an equal and opposite force is exerted on the rocket, propelling it forward. The total momentum of the system (rocket + expelled gases) remains constant.
This worksheet provides a solid foundation for understanding the conservation of momentum. Remember to always consider the system, its closed nature, and the vector nature of momentum when solving problems. Further exploration of elastic and inelastic collisions can enhance your understanding.
