An Object Has A Velocity Of $8 , \text M/s}$ And A Kinetic Energy Of $480 , \text{J}$. What Is The Mass Of The Object?(Formula $K E = \frac{1 {2} M V^2$)A. 7.5 Kg B. 15 Kg C. 60 Kg D. 120 Kg

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Understanding Kinetic Energy and Its Formula

Kinetic energy is a fundamental concept in physics that describes the energy an object possesses due to its motion. The formula for kinetic energy is given by KE=12mv2K E = \frac{1}{2} m v^2, where mm is the mass of the object and vv is its velocity. In this article, we will use this formula to calculate the mass of an object given its kinetic energy and velocity.

Given Information

We are given that an object has a velocity of $8 , \text{m/s}$ and a kinetic energy of $480 , \text{J}$. Our goal is to find the mass of the object using the kinetic energy formula.

Applying the Kinetic Energy Formula

To find the mass of the object, we can rearrange the kinetic energy formula to solve for mm. We start with the formula:

KE=12mv2K E = \frac{1}{2} m v^2

We can rearrange this formula to isolate mm by multiplying both sides by 2 and then dividing by v2v^2:

m=2KEv2m = \frac{2 K E}{v^2}

Substituting Given Values

Now that we have the formula to solve for mm, we can substitute the given values for kinetic energy and velocity:

m=2⋅480 J(8 m/s)2m = \frac{2 \cdot 480 \, \text{J}}{(8 \, \text{m/s})^2}

Calculating Mass

To find the mass of the object, we can simplify the expression:

m=960 J64 m2/s2m = \frac{960 \, \text{J}}{64 \, \text{m}^2/\text{s}^2}

m=96064 kgm = \frac{960}{64} \, \text{kg}

m=15 kgm = 15 \, \text{kg}

Conclusion

Using the kinetic energy formula, we have calculated the mass of the object to be 15 kg15 \, \text{kg}. This is the correct answer, and we can see that it matches one of the options provided.

Discussion

The kinetic energy formula is a fundamental concept in physics that describes the energy an object possesses due to its motion. By rearranging the formula to solve for mass, we can use it to calculate the mass of an object given its kinetic energy and velocity. In this article, we have demonstrated how to apply the kinetic energy formula to solve a problem and arrive at the correct answer.

Common Mistakes

When solving problems involving kinetic energy, it's essential to remember to use the correct formula and to rearrange it to solve for the desired variable. In this case, we rearranged the formula to solve for mass, but we could have also used it to solve for velocity or kinetic energy. It's also crucial to ensure that the units are correct and that we are using the correct values for the given variables.

Real-World Applications

The kinetic energy formula has numerous real-world applications, including:

  • Designing vehicles: By understanding the kinetic energy of a vehicle, designers can optimize its performance and safety features.
  • Calculating energy consumption: By knowing the kinetic energy of an object, we can calculate the energy it consumes and optimize its energy efficiency.
  • Predicting motion: By understanding the kinetic energy of an object, we can predict its motion and behavior in various scenarios.

Conclusion

In conclusion, the kinetic energy formula is a powerful tool for calculating the mass of an object given its kinetic energy and velocity. By rearranging the formula to solve for mass, we can use it to solve a wide range of problems and arrive at the correct answer. Whether you're a student, a researcher, or an engineer, understanding the kinetic energy formula is essential for making accurate calculations and predictions in various fields.

Final Answer

The final answer is: 15\boxed{15}

Understanding Kinetic Energy and Mass

Kinetic energy is a fundamental concept in physics that describes the energy an object possesses due to its motion. The formula for kinetic energy is given by KE=12mv2K E = \frac{1}{2} m v^2, where mm is the mass of the object and vv is its velocity. In this article, we will explore the relationship between kinetic energy and mass through a series of questions and answers.

Q: What is kinetic energy, and how is it related to mass?

A: Kinetic energy is the energy an object possesses due to its motion. The formula for kinetic energy is given by KE=12mv2K E = \frac{1}{2} m v^2, where mm is the mass of the object and vv is its velocity. This means that kinetic energy is directly proportional to the mass of the object and the square of its velocity.

Q: How can I calculate the mass of an object given its kinetic energy and velocity?

A: To calculate the mass of an object, you can use the kinetic energy formula and rearrange it to solve for mass. The formula is:

m=2KEv2m = \frac{2 K E}{v^2}

Q: What are some common mistakes to avoid when calculating kinetic energy and mass?

A: Some common mistakes to avoid include:

  • Incorrect units: Make sure to use the correct units for kinetic energy (Joules) and velocity (meters per second).
  • Incorrect values: Double-check that you are using the correct values for kinetic energy and velocity.
  • Incorrect formula: Use the correct formula for kinetic energy, which is KE=12mv2K E = \frac{1}{2} m v^2.

Q: What are some real-world applications of kinetic energy and mass?

A: Some real-world applications of kinetic energy and mass include:

  • Designing vehicles: By understanding the kinetic energy of a vehicle, designers can optimize its performance and safety features.
  • Calculating energy consumption: By knowing the kinetic energy of an object, we can calculate the energy it consumes and optimize its energy efficiency.
  • Predicting motion: By understanding the kinetic energy of an object, we can predict its motion and behavior in various scenarios.

Q: Can I use the kinetic energy formula to calculate the velocity of an object given its mass and kinetic energy?

A: Yes, you can use the kinetic energy formula to calculate the velocity of an object given its mass and kinetic energy. To do this, you can rearrange the formula to solve for velocity:

v=2KEmv = \sqrt{\frac{2 K E}{m}}

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

A: Kinetic energy and potential energy are two different forms of energy. 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 configuration. The two forms of energy are related by the law of conservation of energy, which states that energy cannot be created or destroyed, only converted from one form to another.

Q: Can I use the kinetic energy formula to calculate the mass of an object given its potential energy and velocity?

A: No, you cannot use the kinetic energy formula to calculate the mass of an object given its potential energy and velocity. The kinetic energy formula is only applicable to objects that are in motion, and potential energy is a different form of energy that is not directly related to motion.

Q: What are some common misconceptions about kinetic energy and mass?

A: Some common misconceptions about kinetic energy and mass include:

  • Kinetic energy is only related to velocity: While velocity is an important factor in determining kinetic energy, mass is also a critical component.
  • Mass is the only factor that affects kinetic energy: Velocity also plays a significant role in determining kinetic energy.
  • Kinetic energy is only applicable to objects in motion: Kinetic energy is a fundamental concept that applies to all objects, regardless of whether they are in motion or not.

Conclusion

In conclusion, the relationship between kinetic energy and mass is a fundamental concept in physics that is essential for understanding the behavior of objects in motion. By understanding the kinetic energy formula and its applications, you can make accurate calculations and predictions in various fields. Whether you're a student, a researcher, or an engineer, mastering the concepts of kinetic energy and mass is crucial for success.

Final Answer

The final answer is: 15\boxed{15}