A 20-kilogram Object Strikes The Ground With 1,960 Joules Of Kinetic Energy After Falling Freely From Rest. How Far Above The Ground Was The Object When It Was Released?A. 10 M B. 14 M C. 98 M D. 200 M
Kinetic Energy and Potential Energy
When an object falls freely from rest, its potential energy is converted into kinetic energy. The potential energy of an object is given by the formula:
U = mgh
Where:
- U is the potential energy
- m is the mass of the object
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- h is the height of the object above the ground
The kinetic energy of an object is given by the formula:
K = (1/2)mv^2
Where:
- K is the kinetic energy
- m is the mass of the object
- v is the velocity of the object
Converting Potential Energy to Kinetic Energy
When an object falls freely from rest, its potential energy is converted into kinetic energy. The total energy of the object remains constant, and the sum of the potential and kinetic energies is equal to the initial potential energy.
E = U + K
Where:
- E is the total energy
- U is the potential energy
- K is the kinetic energy
Solving for Height
We are given that the object strikes the ground with 1,960 joules of kinetic energy. We can use the formula for kinetic energy to solve for the velocity of the object:
K = (1/2)mv^2
Rearranging the formula to solve for velocity, we get:
v = sqrt((2K)/m)
Substituting the given values, we get:
v = sqrt((2*1960)/20)
v = sqrt(196)
v = 14 m/s
Now that we have the velocity of the object, we can use the formula for kinetic energy to solve for the height:
K = (1/2)mv^2
Rearranging the formula to solve for height, we get:
h = v^2 / (2g)
Substituting the given values, we get:
h = (14^2) / (2*9.8)
h = 196 / 19.6
h = 10 m
Conclusion
Therefore, the object was released from a height of 10 meters above the ground.
Answer
The correct answer is A. 10 m.
Additional Information
It's worth noting that the object's velocity increases as it falls, and the kinetic energy increases as the velocity increases. The potential energy is converted into kinetic energy as the object falls, and the total energy remains constant.
Real-World Applications
This concept is important in many real-world applications, such as:
- Aerospace Engineering: Understanding the physics of falling objects is crucial in designing and testing aircraft and spacecraft.
- Mechanical Engineering: The concept of kinetic energy and potential energy is used in the design of mechanical systems, such as gears and pulleys.
- Civil Engineering: The concept of potential energy and kinetic energy is used in the design of buildings and bridges.
Conclusion
Q: What is the difference between potential energy and kinetic energy?
A: Potential energy is the energy an object has due to its position or state, while kinetic energy is the energy an object has due to its motion.
Q: How is potential energy converted into kinetic energy?
A: Potential energy is converted into kinetic energy when an object falls freely from rest. The potential energy is converted into kinetic energy as the object gains speed.
Q: What is the formula for kinetic energy?
A: The formula for kinetic energy is:
K = (1/2)mv^2
Where:
- K is the kinetic energy
- m is the mass of the object
- v is the velocity of the object
Q: What is the formula for potential energy?
A: The formula for potential energy is:
U = mgh
Where:
- U is the potential energy
- m is the mass of the object
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- h is the height of the object above the ground
Q: How is the total energy of an object calculated?
A: The total energy of an object is calculated by adding the potential energy and kinetic energy:
E = U + K
Where:
- E is the total energy
- U is the potential energy
- K is the kinetic energy
Q: What is the relationship between velocity and kinetic energy?
A: The velocity of an object is directly proportional to the square root of its kinetic energy. This means that as the kinetic energy increases, the velocity also increases.
Q: What is the relationship between height and potential energy?
A: The height of an object is directly proportional to its potential energy. This means that as the height increases, the potential energy also increases.
Q: What is the significance of the acceleration due to gravity (g)?
A: The acceleration due to gravity (g) is a constant that represents the rate at which an object falls towards the ground. It is approximately 9.8 m/s^2 on Earth.
Q: How is the kinetic energy of an object affected by its mass?
A: The kinetic energy of an object is directly proportional to its mass. This means that as the mass increases, the kinetic energy also increases.
Q: How is the potential energy of an object affected by its height?
A: The potential energy of an object is directly proportional to its height. This means that as the height increases, the potential energy also increases.
Q: What is the relationship between kinetic energy and potential energy?
A: The kinetic energy and potential energy of an object are related by the equation:
E = U + K
Where:
- E is the total energy
- U is the potential energy
- K is the kinetic energy
This equation shows that the total energy of an object is the sum of its potential energy and kinetic energy.
Q: What is the significance of the concept of energy conservation?
A: The concept of energy conservation states that the total energy of an isolated system remains constant over time. This means that the sum of the potential energy and kinetic energy of an object remains constant as it falls towards the ground.
Q: How is the concept of energy conservation applied in real-world situations?
A: The concept of energy conservation is applied in many real-world situations, such as:
- Aerospace Engineering: Understanding the conservation of energy is crucial in designing and testing aircraft and spacecraft.
- Mechanical Engineering: The concept of energy conservation is used in the design of mechanical systems, such as gears and pulleys.
- Civil Engineering: The concept of energy conservation is used in the design of buildings and bridges.
Conclusion
In conclusion, the concept of energy conservation is a fundamental principle in physics that states that the total energy of an isolated system remains constant over time. The kinetic energy and potential energy of an object are related by the equation E = U + K, and the concept of energy conservation is applied in many real-world situations.