Type The Correct Answer In The Box. Round Your Answer To The Nearest Whole Number.Dina Has A Mass Of 50 Kilograms And Is Waiting At The Top Of A Ski Slope That's 5 Meters High.The Maximum Kinetic Energy She Can Reach When She Skis To The Bottom Of The
Introduction
When it comes to skiing, speed and kinetic energy are crucial factors that determine the thrill and excitement of the experience. As Dina waits at the top of a 5-meter high ski slope, she's about to embark on a journey that will test her skills and push her to the limit. But have you ever wondered what factors contribute to her maximum kinetic energy as she skis to the bottom of the slope? In this article, we'll delve into the world of physics and explore the concepts that govern the motion of objects, including the conversion of potential energy to kinetic energy.
Understanding Potential and Kinetic Energy
Before we dive into the specifics of Dina's skiing adventure, let's take a step back and understand the fundamental concepts of potential and kinetic energy. Potential energy is the energy an object possesses due to its position or configuration, while kinetic energy is the energy an object possesses due to its motion.
Potential Energy
Potential energy is a measure of the energy an object has due to its position or configuration. In the case of Dina, her potential energy is stored in her body as she stands at the top of the ski slope. This energy is due to her mass (50 kilograms) and the height of the slope (5 meters). The formula for potential energy is:
PE = mgh
Where:
- PE is the potential energy
- m is the mass of the object (in kilograms)
- g is the acceleration due to gravity (approximately 9.8 meters per second squared)
- h is the height of the object (in meters)
Kinetic Energy
Kinetic energy, on the other hand, is the energy an object possesses due to its motion. As Dina skis down the slope, her potential energy is converted into kinetic energy. The formula for kinetic energy is:
KE = 0.5mv^2
Where:
- KE is the kinetic energy
- m is the mass of the object (in kilograms)
- v is the velocity of the object (in meters per second)
The Conversion of Potential to Kinetic Energy
As Dina skis down the slope, her potential energy is converted into kinetic energy. This conversion occurs due to the force of gravity acting on her body. The force of gravity causes her to accelerate downward, resulting in an increase in her velocity. As her velocity increases, her kinetic energy also increases.
Calculating the Maximum Kinetic Energy
Now that we've understood the concepts of potential and kinetic energy, let's calculate the maximum kinetic energy Dina can reach as she skis to the bottom of the slope. We'll use the following values:
- Mass (m) = 50 kilograms
- Height (h) = 5 meters
- Acceleration due to gravity (g) = 9.8 meters per second squared
Using the formula for potential energy, we can calculate the initial potential energy of Dina:
PE = mgh = 50 kg x 9.8 m/s^2 x 5 m = 2450 J
As Dina skis down the slope, her potential energy is converted into kinetic energy. We can calculate the maximum kinetic energy using the formula:
KE = 0.5mv^2
However, we need to find the maximum velocity (v) that Dina can reach. To do this, we'll use the conservation of energy principle, which states that the total energy of an isolated system remains constant over time. In this case, the total energy is the sum of the potential energy and the kinetic energy.
Conservation of Energy
The conservation of energy principle can be expressed as:
PE + KE = constant
Since the total energy remains constant, we can set up the following equation:
2450 J + 0.5mv^2 = constant
We can simplify this equation by substituting the value of the constant (2450 J) and solving for v:
0.5mv^2 = 2450 J - 2450 J 0.5mv^2 = 0
However, this equation is not solvable, as it results in a zero value for the kinetic energy. This is because the kinetic energy is zero when the velocity is zero. To find the maximum kinetic energy, we need to consider the case where the velocity is maximum.
Maximum Velocity
The maximum velocity that Dina can reach occurs when she has converted all of her potential energy into kinetic energy. At this point, her kinetic energy is maximum, and her velocity is also maximum.
Using the conservation of energy principle, we can set up the following equation:
PE + KE = constant
Substituting the values, we get:
2450 J + 0.5mv^2 = constant
Simplifying this equation, we get:
0.5mv^2 = 2450 J
Solving for v, we get:
v = sqrt(2 x 2450 J / m) = sqrt(4900 J / 50 kg) = 7.1 m/s
Now that we have the maximum velocity, we can calculate the maximum kinetic energy:
KE = 0.5mv^2 = 0.5 x 50 kg x (7.1 m/s)^2 = 1257 J
Conclusion
In this article, we've explored the concepts of potential and kinetic energy and how they relate to Dina's skiing adventure. We've calculated the maximum kinetic energy she can reach as she skis to the bottom of the slope, using the conservation of energy principle. The maximum kinetic energy is approximately 1257 J.
Discussion
What do you think is the most important factor that contributes to Dina's maximum kinetic energy? Is it her mass, the height of the slope, or something else? Share your thoughts in the comments below!
References
- [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
- [2] Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.
Answer
Introduction
In our previous article, we explored the concepts of potential and kinetic energy and how they relate to Dina's skiing adventure. We calculated the maximum kinetic energy she can reach as she skis to the bottom of the slope. But we know that there are many more questions that our readers might have. In this article, we'll answer some of the most frequently asked questions about kinetic energy and skiing.
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 as it moves through space.
Q: How is kinetic energy related to potential energy?
A: Kinetic energy is related to potential energy through the conservation of energy principle. When an object is at rest, it has potential energy due to its position or configuration. As it begins to move, its potential energy is converted into kinetic energy.
Q: What factors contribute to an object's kinetic energy?
A: An object's kinetic energy is determined by its mass and velocity. The more massive an object is, the more kinetic energy it will have. The faster an object moves, the more kinetic energy it will have.
Q: Can you give an example of how kinetic energy is used in real-life situations?
A: Yes, kinetic energy is used in many real-life situations. For example, when you're driving a car, the kinetic energy of the car is converted into the energy of the motion. When you're skiing or snowboarding, the kinetic energy of your body is converted into the energy of the motion.
Q: How does the height of a slope affect an object's kinetic energy?
A: The height of a slope affects an object's kinetic energy by determining the amount of potential energy it has. The higher the slope, the more potential energy the object will have, and the more kinetic energy it will have when it reaches the bottom.
Q: Can you calculate the kinetic energy of an object using a formula?
A: Yes, the kinetic energy of an object can be calculated using the formula:
KE = 0.5mv^2
Where:
- KE is the kinetic energy
- m is the mass of the object
- v is the velocity of the object
Q: What is the maximum kinetic energy that an object can reach?
A: The maximum kinetic energy that an object can reach is determined by the amount of potential energy it has. If an object has a large amount of potential energy, it will have a large amount of kinetic energy when it reaches the bottom of a slope.
Q: Can you give an example of how to calculate the maximum kinetic energy of an object?
A: Yes, let's use the example of Dina skiing down a 5-meter high slope. We can calculate the maximum kinetic energy she can reach using the formula:
KE = 0.5mv^2
Where:
- KE is the kinetic energy
- m is the mass of Dina (50 kg)
- v is the velocity of Dina (7.1 m/s)
Plugging in the values, we get:
KE = 0.5 x 50 kg x (7.1 m/s)^2 = 1257 J
Conclusion
In this article, we've answered some of the most frequently asked questions about kinetic energy and skiing. We've explored the concepts of potential and kinetic energy and how they relate to Dina's skiing adventure. We've also calculated the maximum kinetic energy she can reach as she skis to the bottom of the slope.
Discussion
What do you think is the most important factor that contributes to an object's kinetic energy? Is it its mass, velocity, or something else? Share your thoughts in the comments below!
References
- [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
- [2] Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.
Answer
The maximum kinetic energy that Dina can reach as she skis to the bottom of the slope is approximately 1257 J.