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

In summary, the only force acting on a 2.9 kg body moving along the positive x-axis is an x component Fx = -6x N, with x in meters. The velocity of the body at x = 3.0 m is 8.0 m/s. To find the velocity at x = 4, you need to use the proper equation, which is (1/2)m(v2^2-3^2). For the total energy of the body at x = 3 and x = 4, you need to use the equation for total energy, which is the sum of kinetic energy and spring potential energy. The proper equation for spring potential energy is (1/2)kx^
  • #1
sciencegeek26
3
0
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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  • #2
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.
 
  • #3
I got it to be -21J but I think I'm using the wrong equation
 
  • #4
sciencegeek26 said:
I got it to be -21J but I think I'm using the wrong equation
What equation are you using?
 
  • #5
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
 
  • #6
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?
 

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

What is spring force?

Spring force is the force exerted by a spring when it is stretched or compressed. It is a restoring force that causes the spring to return to its original length when the external force is removed.

How is spring force calculated?

Spring force is calculated using Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The formula for spring force is F = -kx, where F is the force, k is the spring constant, and x is the displacement.

What factors affect spring force?

The spring force is affected by the spring constant, which is determined by the material and shape of the spring, as well as the displacement from the equilibrium position. The force also depends on the direction of the displacement, as the spring will exert a different force when compressed versus when stretched.

How does spring force relate to other types of forces?

Spring force is a type of contact force, as it requires physical contact between the spring and the object it is acting upon. It is also a conservative force, meaning that the work done by the spring force is independent of the path taken.

What are some real-world applications of spring force?

Spring force is used in many everyday objects, such as car suspension systems, trampolines, and door hinges. It is also used in scientific experiments and studies, such as in the study of elasticity and in the design of various mechanical devices.

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