A 40 Kg Dog Is Sitting On Top Of A Hillside And Has A Potential Energy Of $1,568 , J$. What Is The Height Of The Hillside? (Use The Formula P E = M G H PE = Mgh PE = M G H .)A. 3.9 M B. 4.0 M C. 39.2 M D. 40.0 M

Introduction

Potential energy is a fundamental concept in physics that describes the stored energy an object possesses due to its position or configuration. In this article, we will explore the relationship between potential energy and height, using the formula $PE = mgh$, where $PE$ is the potential energy, $m$ is the mass of the object, $g$ is the acceleration due to gravity, and $h$ is the height of the object above a reference point.

The Formula: $PE = mgh$

The formula $PE = mgh$ is a fundamental equation in physics that relates the potential energy of an object to its mass, the acceleration due to gravity, and its height. This equation is a direct result of the work-energy theorem, which states that the net work done on an object is equal to its change in kinetic energy. In the case of potential energy, the work done is due to the object's position or configuration, and the change in kinetic energy is zero.

The Given Problem

In this problem, we are given a 40 kg dog sitting on top of a hillside with a potential energy of $1,568 \, J$. We are asked to find the height of the hillside using the formula $PE = mgh$.

Step 1: Identify the Given Values

• Mass of the dog ($m$): $40 \, kg$
• Potential energy ($PE$): $1,568 \, J$
• Acceleration due to gravity ($g$): $9.8 \, m/s^2$ (approximately)

Step 2: Rearrange the Formula to Solve for Height

To solve for height ($h$), we need to rearrange the formula $PE = mgh$ to isolate $h$. We can do this by dividing both sides of the equation by $mg$:

$h = \frac{PE}{mg}$

Step 3: Plug in the Given Values

Now that we have the rearranged formula, we can plug in the given values:

$h = \frac{1,568 \, J}{(40 \, kg)(9.8 \, m/s^2)}$

Step 4: Calculate the Height

To calculate the height, we can perform the division:

$h = \frac{1,568 \, J}{392 \, kg \cdot m/s^2}$

$h = 4.0 \, m$

Conclusion

In this article, we used the formula $PE = mgh$ to find the height of a hillside given a 40 kg dog with a potential energy of $1,568 \, J$. By rearranging the formula to solve for height and plugging in the given values, we found that the height of the hillside is approximately $4.0 \, m$.

Discussion

This problem is a classic example of how potential energy is related to height. The formula $PE = mgh$ is a fundamental concept in physics that describes the stored energy an object possesses due to its position or configuration. In this case, the dog's potential energy is due to its height above the reference point, and we can use the formula to find the height.

Answer

The correct answer is:

• B. 4.0 m

Additional Information

• The acceleration due to gravity ($g$) is approximately $9.8 \, m/s^2$ on Earth's surface.
• The potential energy ($PE$) is a measure of the stored energy an object possesses due to its position or configuration.
• The formula $PE = mgh$ is a fundamental equation in physics that relates the potential energy of an object to its mass, the acceleration due to gravity, and its height.
  A 40 kg dog is sitting on top of a hillside and has a potential energy of $1,568 , J$. What is the height of the hillside? (Use the formula $PE = mgh$.)A. 3.9 m B. 4.0 m C. 39.2 m D. 40.0 m

Q: What is potential energy?

A: Potential energy is a measure of the stored energy an object possesses due to its position or configuration. In the case of a dog sitting on top of a hillside, the potential energy is due to its height above the reference point.

Q: What is the formula for potential energy?

A: The formula for potential energy is $PE = mgh$, where $PE$ is the potential energy, $m$ is the mass of the object, $g$ is the acceleration due to gravity, and $h$ is the height of the object above a reference point.

Q: What is the acceleration due to gravity?

A: The acceleration due to gravity ($g$) is approximately $9.8 \, m/s^2$ on Earth's surface.

Q: How do we use the formula $PE = mgh$ to find the height of the hillside?

A: To find the height of the hillside, we need to rearrange the formula $PE = mgh$ to isolate $h$. We can do this by dividing both sides of the equation by $mg$:

$h = \frac{PE}{mg}$

Q: What are the given values in this problem?

A: The given values are:

• Mass of the dog ($m$): $40 \, kg$
• Potential energy ($PE$): $1,568 \, J$
• Acceleration due to gravity ($g$): $9.8 \, m/s^2$ (approximately)

Q: How do we plug in the given values into the formula?

A: We can plug in the given values into the formula $h = \frac{PE}{mg}$:

$h = \frac{1,568 \, J}{(40 \, kg)(9.8 \, m/s^2)}$

Q: What is the height of the hillside?

A: To find the height of the hillside, we can perform the division:

$h = \frac{1,568 \, J}{392 \, kg \cdot m/s^2}$

$h = 4.0 \, m$

Q: What is the correct answer?

A: The correct answer is:

• B. 4.0 m

Additional Q&A

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

A: The potential energy of an object is directly proportional to its height above a reference point.

Q: Can we use the formula $PE = mgh$ to find the height of an object on a different planet?

A: Yes, we can use the formula $PE = mgh$ to find the height of an object on a different planet, but we need to use the acceleration due to gravity on that planet.

Q: What is the unit of potential energy?

A: The unit of potential energy is joules (J).

Q: Can we use the formula $PE = mgh$ to find the potential energy of an object?

A: Yes, we can use the formula $PE = mgh$ to find the potential energy of an object, but we need to know the mass of the object, the acceleration due to gravity, and the height of the object above a reference point.