Select The Correct Answer.A Car Moving With A Velocity Of 20 Meters/second Has $1.8 \times 10^5$ Joules Of Kinetic Energy. What Is The Mass Of The Car?A. $4.6 \times 10^2$ Kilograms B. \$9.0 \times 10^2$[/tex\]

Introduction

Kinetic energy is a fundamental concept in physics that describes the energy of an object in motion. It is a measure of the energy an object possesses due to its motion. In this article, we will explore the relationship between kinetic energy and mass, and use this relationship to solve a problem involving a car moving at a velocity of 20 meters/second.

Kinetic Energy Formula

The kinetic energy of an object is given by the formula:

$$KE = \frac{1}{2}mv^2$$

where $KE$ is the kinetic energy, $m$ is the mass of the object, and $v$ is the velocity of the object.

Problem Statement

A car moving with a velocity of 20 meters/second has $1.8 \times 10^5$ joules of kinetic energy. What is the mass of the car?

Solution

To solve this problem, we can use the kinetic energy formula and rearrange it to solve for mass:

$$m = \frac{2KE}{v^2}$$

Substituting the given values, we get:

$$m = \frac{2 \times 1.8 \times 10^5}{(20)^2}$$

$$m = \frac{3.6 \times 10^5}{400}$$

$$m = 9.0 \times 10^2$$

Therefore, the mass of the car is $9.0 \times 10^2$ kilograms.

Discussion

The relationship between kinetic energy and mass is a fundamental concept in physics. The kinetic energy of an object is directly proportional to its mass and the square of its velocity. This means that as the mass of an object increases, its kinetic energy also increases, assuming the velocity remains constant.

In this problem, we used the kinetic energy formula to solve for the mass of the car. We rearranged the formula to solve for mass and substituted the given values to find the answer.

Conclusion

In conclusion, the mass of the car is $9.0 \times 10^2$ kilograms. This problem demonstrates the relationship between kinetic energy and mass, and shows how to use the kinetic energy formula to solve for mass.

Additional Information

• The kinetic energy of an object is a measure of its energy in motion.
• The kinetic energy formula is $KE = \frac{1}{2}mv^2$.
• The mass of an object is directly proportional to its kinetic energy and the square of its velocity.
• The kinetic energy formula can be rearranged to solve for mass: $m = \frac{2KE}{v^2}$.

References

• Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
• Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.

Related Topics

• Kinetic energy and potential energy
• Work and energy
• Momentum and force
• Rotational motion and torque

Practice Problems

1. A car moving with a velocity of 30 meters/second has $2.4 \times 10^5$ joules of kinetic energy. What is the mass of the car?
2. A bicycle moving with a velocity of 10 meters/second has $1.0 \times 10^3$ joules of kinetic energy. What is the mass of the bicycle?
3. A ball moving with a velocity of 20 meters/second has $1.2 \times 10^4$ joules of kinetic energy. What is the mass of the ball?
   Kinetic Energy and Mass: Q&A =============================

Introduction

In our previous article, we explored the relationship between kinetic energy and mass, and used this relationship to solve a problem involving a car moving at a velocity of 20 meters/second. In this article, we will answer some frequently asked questions about kinetic energy and mass.

Q: What is kinetic energy?

A: Kinetic energy is the energy an object possesses due to its motion. It is a measure of the energy an object has because it is moving.

Q: What is the formula for kinetic energy?

A: The formula for kinetic energy is:

$$KE = \frac{1}{2}mv^2$$

where $KE$ is the kinetic energy, $m$ is the mass of the object, and $v$ is the velocity of the object.

Q: How is kinetic energy related to mass?

A: Kinetic energy is directly proportional to the mass of an object and the square of its velocity. This means that as the mass of an object increases, its kinetic energy also increases, assuming the velocity remains constant.

Q: Can you give an example of how to use the kinetic energy formula to solve a problem?

A: Let's say we have a car moving with a velocity of 20 meters/second and we want to find its kinetic energy. We can use the kinetic energy formula:

$$KE = \frac{1}{2}mv^2$$

We know the velocity of the car is 20 meters/second, but we don't know its mass. Let's say we want to find the mass of the car. We can rearrange the formula to solve for mass:

$$m = \frac{2KE}{v^2}$$

Substituting the given values, we get:

$$m = \frac{2 \times 1.8 \times 10^5}{(20)^2}$$

$$m = \frac{3.6 \times 10^5}{400}$$

$$m = 9.0 \times 10^2$$

Therefore, the mass of the car is $9.0 \times 10^2$ kilograms.

Q: What is the difference between kinetic energy and potential energy?

A: Kinetic energy is the energy an object possesses due to its motion, while potential energy is the energy an object possesses due to its position or state. For example, a ball at the top of a hill has potential energy due to its position, while a ball rolling down the hill has kinetic energy due to its motion.

Q: Can you give an example of how to use the kinetic energy formula to solve a problem involving potential energy?

A: Let's say we have a ball at the top of a hill with a height of 10 meters. We want to find the potential energy of the ball. We can use the formula for potential energy:

$$PE = mgh$$

where $PE$ is the potential energy, $m$ is the mass of the ball, $g$ is the acceleration due to gravity, and $h$ is the height of the ball.

We know the height of the ball is 10 meters, but we don't know its mass. Let's say we want to find the mass of the ball. We can rearrange the formula to solve for mass:

$$m = \frac{PE}{gh}$$

Substituting the given values, we get:

$$m = \frac{1.0 \times 10^3}{9.8 \times 10}{10}$$

$$m = \frac{1.0 \times 10^3}{98}$$

$$m = 1.0 \times 10^2$$

Therefore, the mass of the ball is $1.0 \times 10^2$ kilograms.

Q: What is the relationship between kinetic energy and momentum?

A: Kinetic energy and momentum are related by the formula:

$$KE = \frac{p^2}{2m}$$

where $KE$ is the kinetic energy, $p$ is the momentum, and $m$ is the mass of the object.

Q: Can you give an example of how to use the kinetic energy formula to solve a problem involving momentum?

A: Let's say we have a car moving with a velocity of 20 meters/second and a momentum of $2.0 \times 10^3$ kg m/s. We want to find its kinetic energy. We can use the kinetic energy formula:

$$KE = \frac{p^2}{2m}$$

We know the momentum of the car is $2.0 \times 10^3$ kg m/s, but we don't know its mass. Let's say we want to find the mass of the car. We can rearrange the formula to solve for mass:

$$m = \frac{p^2}{2KE}$$

Substituting the given values, we get:

$$m = \frac{(2.0 \times 10^3)^2}{2 \times 1.8 \times 10^5}$$

$$m = \frac{4.0 \times 10^6}{3.6 \times 10^5}$$

$$m = 1.1 \times 10^2$$

Therefore, the mass of the car is $1.1 \times 10^2$ kilograms.

Conclusion

In conclusion, kinetic energy and mass are related by the formula:

$$KE = \frac{1}{2}mv^2$$

We can use this formula to solve problems involving kinetic energy and mass. We can also use the kinetic energy formula to solve problems involving potential energy and momentum.

Additional Information

• The kinetic energy of an object is a measure of its energy in motion.
• The kinetic energy formula is $KE = \frac{1}{2}mv^2$.
• The mass of an object is directly proportional to its kinetic energy and the square of its velocity.
• The kinetic energy formula can be rearranged to solve for mass: $m = \frac{2KE}{v^2}$.

References

• Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
• Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.

Related Topics

• Kinetic energy and potential energy
• Work and energy
• Momentum and force
• Rotational motion and torque

Practice Problems

1. A car moving with a velocity of 30 meters/second has $2.4 \times 10^5$ joules of kinetic energy. What is the mass of the car?
2. A bicycle moving with a velocity of 10 meters/second has $1.0 \times 10^3$ joules of kinetic energy. What is the mass of the bicycle?
3. A ball moving with a velocity of 20 meters/second has $1.2 \times 10^4$ joules of kinetic energy. What is the mass of the ball?