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

Mar 10, 2025 by ADMIN 209 views

$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?$

Understanding Kinetic Energy

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 $KE = \frac{1}{2} m v^2$ , where $m$ is the mass of the object and $v$ is its velocity. In this problem, we are given the kinetic energy ( $480 \, \text{J}$ ) and the velocity ( $8 \, \text{m/s}$ ) of an object, and we need to find its mass.

Applying the Kinetic Energy Formula

To find the mass of the object, we can rearrange the kinetic energy formula to solve for $m$ . We start with the formula $KE = \frac{1}{2} m v^2$ . Multiplying both sides by 2, we get $2KE = m v^2$ . Now, dividing both sides by $v^2$ , we obtain $m = \frac{2KE}{v^2}$ .

Substituting Given Values

We are given that the kinetic energy ( $KE$ ) is $480 \, \text{J}$ and the velocity ( $v$ ) is $8 \, \text{m/s}$ . Substituting these values into the formula, we get $m = \frac{2(480 \, \text{J})}{(8 \, \text{m/s})^2}$ .

Calculating the Mass

Now, let's calculate the mass of the object. Plugging in the values, we get $m = \frac{2(480 \, \text{J})}{(8 \, \text{m/s})^2} = \frac{960 \, \text{J}}{64 \, \text{m}^2/\text{s}^2} = 15 \, \text{kg}$ .

Conclusion

Therefore, the mass of the object is $15 \, \text{kg}$ .

Discussion

This problem demonstrates the application of the kinetic energy formula to find the mass of an object. The formula $KE = \frac{1}{2} m v^2$ is a fundamental concept in physics that relates the kinetic energy of an object to its mass and velocity. By rearranging the formula to solve for $m$ , we can find the mass of an object given its kinetic energy and velocity.

Common Mistakes

When solving this problem, it's essential to remember to multiply both sides of the equation by 2 to eliminate the fraction, and then divide both sides by $v^2$ to solve for $m$ . Additionally, make sure to substitute the given values correctly into the formula.

Real-World Applications

Understanding the kinetic energy formula and its application to find the mass of an object has numerous real-world implications. For instance, in the field of engineering, knowing the mass of an object can help designers and engineers optimize the performance of machines and systems. In the field of physics, understanding the kinetic energy formula is crucial for analyzing the motion of objects and predicting their behavior.

Additional Resources

For further reading on the kinetic energy formula and its applications, we recommend the following resources:

Final Answer

The final answer is: $\boxed{15}$

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 $KE = \frac{1}{2} m v^2$ , where $m$ is the mass of the object and $v$ is its velocity. In this article, we will answer some common questions related to 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 of its velocity.

Q: What is the formula for kinetic energy?

A: The formula for kinetic energy is given by $KE = \frac{1}{2} m v^2$ , where $m$ is the mass of the object and $v$ is its velocity.

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

A: To find the mass of an object, you can rearrange the kinetic energy formula to solve for $m$ . You start with the formula $KE = \frac{1}{2} m v^2$ . Multiplying both sides by 2, you get $2KE = m v^2$ . Now, dividing both sides by $v^2$ , you obtain $m = \frac{2KE}{v^2}$ .

Q: What is the unit of kinetic energy?

A: The unit of kinetic energy is typically measured in joules (J).

Q: What is the unit of mass?

A: The unit of mass is typically measured in kilograms (kg).

Q: Can kinetic energy be negative?

A: No, kinetic energy cannot be negative. Kinetic energy is a measure of the energy an object has due to its motion, and it is always positive.

Q: Can an object have zero kinetic energy?

A: Yes, an object can have zero kinetic energy if it is at rest. When an object is at rest, its velocity is zero, and therefore its kinetic energy is also zero.

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

A: The kinetic energy of an object is directly proportional to the square of its velocity. This means that as the velocity of an object increases, its kinetic energy also increases.

Q: Can kinetic energy be transferred from one object to another?

A: Yes, kinetic energy can be transferred from one object to another through collisions or other interactions.

Q: What is the significance of kinetic energy in real-world applications?

A: Kinetic energy has numerous real-world applications, including in the design of machines and systems, in the analysis of motion, and in the prediction of behavior.

Q: What are some common mistakes to avoid when working with kinetic energy?

A: Some common mistakes to avoid when working with kinetic energy include:

Failing to multiply both sides of the equation by 2 to eliminate the fraction
Failing to divide both sides of the equation by $v^2$ to solve for $m$
Substituting the wrong values into the formula
Failing to consider the units of the variables

Conclusion

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 $KE = \frac{1}{2} m v^2$ , where $m$ is the mass of the object and $v$ is its velocity. By understanding the kinetic energy formula and its applications, we can better analyze the motion of objects and predict their behavior.

Additional Resources

For further reading on kinetic energy and mass, we recommend the following resources:

Final Answer

The final answer is: $\boxed{15}$