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Chapter 2: Problem 68

Which of the following statements is true based on the equation for momentum? A. If mass gets doubled, momentum will get halved. B. If velocity gets doubled, momentum will get halved. C. If both mass and velocity get doubled, momentum will increase by four times. D. If both mass and velocity get halved, momentum will increase by four times.

Short Answer

Expert verified
Statement C is true: If both mass and velocity get doubled, momentum will increase by four times.

Step by step solution

01

- Understand the momentum formula

The momentum (p) of an object is given by the formula: \( p = m \times v \) where \( m \) is the mass and \( v \) is the velocity.
02

- Analyze statement A

Statement A: If mass gets doubled, momentum will get halved. According to the momentum formula, if mass \( m \) is doubled and velocity \( v \) remains constant, momentum \( p \) should double, not halve.
03

- Analyze statement B

Statement B: If velocity gets doubled, momentum will get halved. According to the momentum formula, if velocity \( v \) is doubled and mass \( m \) remains constant, momentum \( p \) should double, not halve.
04

- Analyze statement C

Statement C: If both mass and velocity get doubled, momentum will increase by four times. Using the momentum formula, doubling both mass \( m \) and velocity \( v \) gives: \( p' = (2m) \times (2v) = 4(m \times v) = 4p \) This statement is true.
05

- Analyze statement D

Statement D: If both mass and velocity get halved, momentum will increase by four times. Using the momentum formula, halving both mass \( m \) and velocity \( v \) gives: \( p' = (0.5m) \times (0.5v) = 0.25(m \times v) = 0.25p \) This means the momentum will be one-quarter of the original, not four times.
06

- Conclusion

After analyzing all the statements, Statement C is the accurate one based on the equation for momentum.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Physics Equations
In physics, equations are essential tools for describing relationships between different physical quantities. One crucial equation is the momentum formula. It shows how mass and velocity combine to determine an object's momentum. Equations in physics help us predict outcomes and explain the behavior of objects. Understanding them allows us to solve problems step-by-step in a logical manner. Many concepts in physics, like acceleration, force, and energy, also use equations. These equations are often simple in form but have profound implications. Knowing how to manipulate these equations is key to mastering physics.
Mass and Velocity Relationship
Mass and velocity are two fundamental properties that directly affect an object's momentum. Mass refers to the amount of matter in an object and is usually measured in kilograms (kg). Velocity is the speed of the object in a particular direction and is measured in meters per second (m/s).

The momentum formula shows a direct relationship: \( p = m \times v \). This means that:
  • If the mass of an object doubles while the velocity stays the same, the momentum also doubles.
  • If the velocity of an object doubles while the mass stays the same, the momentum doubles.

Doubled mass or velocity multiplies momentum by two. Doubling both mass and velocity quadruples the momentum. Changes in mass and velocity have a linear impact on momentum. This relationship helps us understand various physical phenomena, like why heavier objects at the same speed have more momentum.
Momentum Calculation
Calculating momentum involves using the formula \( p = m \times v \). To determine the momentum (p) of an object, you need to know its mass (m) and velocity (v). Here’s a quick guide to calculate:

  • Identify the mass (m) of the object: This is the amount of matter in the object and is measured in kilograms.
  • Determine the velocity (v) of the object: This is how fast the object is moving in a certain direction and is measured in meters per second.
  • Multiply the mass by the velocity: Use the equation \( p = m \times v \) to find the momentum.

For example, if an object has a mass of 2 kg and a velocity of 3 m/s, its momentum would be \( p = 2 \times 3 = 6 \) kg·m/s. Understanding and using this calculation helps solve many physics problems related to motion, collisions, and other dynamics.

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Most popular questions from this chapter

If the speed of an object is doubled, then its kinetic energy is \begin{tabular}{|l|l|} \hline Select... & . \\ \hline doubled \\ \hline quadrupled \\ \hline reduced by half \\ \hline tripled \\ \hline \end{tabular}

Oxygen will be \begin{tabular}{|l|l|} \hline Select... & voluble in cold water than \\ \hline more & \\ \hline less \end{tabular} in hot water.

A book is placed on a dashboard of a car that is stopped at a traffic light. As the car starts to move forward, the book slides off the dashboard. Pick the most correct explanation for the book sliding off the dashboard. A. There is grease on the dashboard, so the book slides off the dashboard. B. Due to inertia, the book slides off the dashboard. C. The book is heavy, so it slides off the dashboard. D. Air resistance made the book move backward.

Which of the following is the best example of Newton's first law of motion? A. Whenever you push against a wall, the wall pushes back. B. When a bat hits a ball, the ball hits the bat. C. A rider on a running horse is thrown forward when the horse stops suddenly. D. A 100-g baseball will accelerate more slowly than a \(50-\mathrm{g}\) baseball because of its greater mass.

Which of the following describes the process of diffusion? A. A substance moves from an area of low concentration to an area of high concentration. B. A substance moves from an area of high concentration to an area of low concentration. C. A substance moves from the center toward two opposite poles. D. A liquid is turned into a gas through the application of heat.
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