Graphs of Position & Kinetic Energy vs. Time: Solving U(x)=7J

In summary, the conversation discusses a potential energy function and the total energy of a particle, with an initial position of 0, being 7 J. The graphs for position vs. time and kinetic energy vs. time are then discussed, with the conclusion that the latter is represented by a cos^2 function due to the relationship between energy, potential energy, and kinetic energy. The use of cos^2 is mathematically derived from this principle, rather than cos(2x).
  • #1
dmayers94
16
0

Homework Statement


A potential energy function is given by U(x) = 4x^2 and I found the total energy to be 7 J. They ask: Graph position vs. time and kinetic energy vs. time using this information and assume that the particle has an initial position of 0.

The Attempt at a Solution


I got the first part correct. It is just a sine curve because the object oscillates and is bounded by the total mechanical energy of 7 J. The second graph, KE vs. time, is a cos^2 function, but I'm not sure why. I know that as the potential energy increases, position increases, and when potential energy is at a max, KE is 0. The shape makes sense to me when I compare it to the position graph, but how did they come up with cos^2 mathematically? Why not cos(2x) instead?
 
Physics news on Phys.org
  • #2
You need to work back from the main principles, to get the reason for using a cos^2 function. What is the main principle between energy, potential energy and kinetic energy? And what is the equation for this relationship?
 

FAQ: Graphs of Position & Kinetic Energy vs. Time: Solving U(x)=7J

What is meant by "Graphs of Position & Kinetic Energy vs. Time"?

These graphs represent the relationship between an object's position and its kinetic energy over a period of time. The position is measured in units of distance, such as meters, and the kinetic energy is measured in units of energy, such as joules.

What is U(x) and how does it relate to the graphs?

U(x) represents the potential energy of the object at a specific position, x. This potential energy can be converted into kinetic energy as the object moves. The graphs show the changes in both potential and kinetic energy over time.

How do you solve for U(x)=7J?

To solve for U(x)=7J, you need to set the potential energy equal to 7 joules and solve for the corresponding position, x. This can be done by using the formula for potential energy, U(x) = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the vertical distance from the reference point.

What does the slope of the position vs. time graph represent?

The slope of the position vs. time graph represents the object's velocity. This is because velocity is the rate of change of an object's position over time.

How can these graphs be useful in understanding the motion of an object?

These graphs can be used to visualize and analyze the motion of an object. By examining the changes in position and kinetic energy over time, we can determine the object's speed, acceleration, and potential energy at any given point. This can help us understand the forces acting on the object and predict its future motion.

Similar threads

Graphing Elastic Potential Energy
Replies
10
Views
1K
Using energy considerations to analyse particle motion
Replies
3
Views
522
Kinetic Energy of a Cylinder Rolling Without Slipping
Replies
21
Views
2K
Finding acceleration from Velocity vs Position graph
Replies
2
Views
3K
Graphing Kinetic Energy of a Toy Car Released from a Compressed Spring
Replies
13
Views
17K
Potential and Kinetic energy equations including drag coefficient
Replies
1
Views
1K
How Do You Graph Kinetic Energy Against Time and Distance?
Replies
6
Views
4K
Conundrums on energy and graphs
Replies
5
Views
998
Obtaining Acceleration from Position vs Time graph
Replies
3
Views
5K
Graphing Oscillating Objects: Can You Find the Spring Constant?
Replies
8
Views
3K

Hot Threads

Recent Insights

Back
Top