Questions and Answers
What is the formula for momentum?
If a dinosaur with a mass of 4,500 kg and a velocity of 12 m/s has positive momentum, what is its calculated momentum?
What is the total momentum before the collision of the dinosaur and the car if the car has negative momentum?
What happens to the total momentum in a closed system after an event like a collision?
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How do you calculate the velocity of a combined object after a collision if its total momentum is known?
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What type of momentum does a stationary object have?
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When a gun fires a bullet, what distinguishes the momentum of the bullet from that of the gun?
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If a 5-gram bullet is fired at a velocity of 120 m/s, what is the bullet's momentum?
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Study Notes
Momentum Basics
- Momentum (p) is defined as the product of an object's mass (m) and its velocity (v): p = m × v.
- Example: A dinosaur with a mass of 4,500 kg traveling at 12 m/s has a momentum of 54,000 kg·m/s.
- Example: A car with a mass of 1,200 kg traveling at 25 m/s has a momentum of 30,000 kg·m/s.
- Momentum is a vector quantity, meaning it has both magnitude and direction.
Positive and Negative Momentum
- If a direction is defined as positive (e.g., right), the dinosaur carries positive momentum and the car negative momentum when heading towards each other.
Conservation of Momentum
- In a closed system, total momentum before an event (like a collision) equals total momentum after the event.
- For the dinosaur and car example, pre-collision momentum is calculated: 54,000 kg·m/s (dinosaur) + (-30,000 kg·m/s) (car) = 24,000 kg·m/s total momentum (to the right).
Post-Collision Velocity
- After their collision, the combined object maintains the total momentum of 24,000 kg·m/s.
- Combined mass of dinosaur and car: 4,500 kg + 1,200 kg = 5,700 kg.
- Using momentum equation: velocity (v) = momentum (p) / mass (m) results in v = 24,000 kg·m/s / 5,700 kg = 4.4 m/s to the right.
Zero Momentum Scenario
- Objects at rest have zero momentum. For example, a stationary gun has zero initial momentum.
- When the gun fires, the bullet gains forward momentum while the gun recoils backward with equal momentum to maintain a total momentum of zero.
Gun and Bullet Example
- A 5-gram bullet (0.005 kg) fired at a velocity of 120 m/s has a momentum of 0.6 kg·m/s.
- For the gun (2 kg), let its recoil velocity be v; its momentum is 2v.
- The equation for the total momentum: 2v + 0.6 = 0 leads to determining the recoil velocity of the gun.
- Rearranging gives: 2v = -0.6, resulting in v = -0.3 m/s (direction opposite to the bullet's momentum).
Momentum Notation
- The symbol for momentum is p, leading to the equation: p = mv.
Momentum Basics
- Momentum (p) is the product of mass (m) and velocity (v): p = m × v.
- A dinosaur with a mass of 4,500 kg traveling at 12 m/s has momentum: 54,000 kg·m/s.
- A car with a mass of 1,200 kg traveling at 25 m/s has momentum: 30,000 kg·m/s.
- Momentum is a vector quantity, meaning it has direction as well as magnitude.
Positive and Negative Momentum
- If a rightward direction is defined as positive, a dinosaur moving right has positive momentum, while a car moving left has negative momentum when approaching each other.
Conservation of Momentum
- In a closed system, total momentum before an event equals total momentum after the event.
- For the dinosaur and car collision, pre-collision momentum is: 54,000 kg·m/s (dinosaur) + (-30,000 kg·m/s) (car) = 24,000 kg·m/s (to the right).
Post-Collision Velocity
- After the collision, the combined object retains momentum of 24,000 kg·m/s.
- The combined mass of the dinosaur and car is: 4,500 kg + 1,200 kg = 5,700 kg.
- Use momentum equation to find velocity: v = 24,000 kg·m/s / 5,700 kg = 4.4 m/s to the right.
Zero Momentum Scenario
- Objects at rest possess zero momentum.
- A stationary gun has zero initial momentum.
- Upon firing, the bullet gains forward momentum while the gun recoils backward with equal momentum, preserving a total momentum of zero.
Gun and Bullet Example
- A bullet weighing 5 grams (0.005 kg) fired at 120 m/s has momentum: 0.6 kg·m/s.
- For the 2 kg gun, if the recoil velocity is v, its momentum is expressed as 2v.
- Setting up the total momentum equation: 2v + 0.6 = 0 allows determination of the gun's recoil velocity.
- Solving gives 2v = -0.6, resulting in v = -0.3 m/s (in the opposite direction of the bullet's momentum).
Momentum Notation
- The symbol for momentum is p.
- The fundamental momentum equation is expressed as: p = mv.
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Description
Test your understanding of momentum, its definition, and its applications. This quiz covers topics such as positive and negative momentum as well as the conservation of momentum in collisions. You'll encounter practical examples to enhance your knowledge.
