What is the total energy of the body at x=4 meters?

AI Thread Summary
The discussion focuses on calculating the total energy of a 2.9 kg body moving along the x-axis under the influence of a force defined by Fx = -6x N. The velocity at x = 3.0 m is given as 8.0 m/s, and participants are trying to determine the velocity at x = 4 m and the position where the velocity will be 5 m/s. There is confusion regarding the correct equations to use for calculating total energy, with participants debating the proper setup for kinetic and potential energy. The total energy should be expressed as the sum of kinetic energy and spring potential energy, indicating a need for clarity on how to correctly apply these formulas. The conversation highlights the importance of using the right equations to accurately solve for the body's energy and velocity.
sciencegeek26
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The only force acting on a 2.9 kg body as it moves along the positive x-axis has an x component Fx = - 6x N, where x is in meters. The velocity of the body at x = 3.0 m is 8.0 m/s.

What is the velocity of the body at x=4?

At what positive value of x will the body have a velocity of 5 m/s?

I got the answer to the second question just fine, which ended up being 5.3. I feel like I just am doing the first one wrong. What is the proper equation for it? I thought it would be
-6/2(4^2-3^2). Or at least that is what my teacher said would give me the correct answer. Alas that is not so. I just need the proper way to do the first one now.
 
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What's the total energy of the body at x = 3 and at x = 4? Set up an equation and then you can solve for the speed.
 
I got it to be -21J but I think I'm using the wrong equation
 
sciencegeek26 said:
I got it to be -21J but I think I'm using the wrong equation
What equation are you using?
 
Doc Al said:
What equation are you using?

(1/2)m(v2^2-3^2)

Instead of 3 being squared should it be 8m/s? Then I would get -69.6J
 
sciencegeek26 said:
(1/2)m(v2^2-3^2)

Instead of 3 being squared should it be 8m/s? Then I would get -69.6J
You need to fix that formula. The total energy is the sum of the kinetic energy and the spring potential energy. How would you express spring potential energy?
 
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