Question Regarding Changes in Kinetic Energy

In summary, the maximum kinetic energy attained by the 4.0 kg body as it moves along the x-axis is 68 J, which occurs at x = 2 m. This is found by using the equation K = 0.5 * m * v^2 and the fact that work is the integral of the function of force in regards to position. The initial kinetic energy is 98 J and the body returns to this value at x = 2 m. The maximum kinetic energy is over 100 J but this cannot be achieved due to the negative force between x = 1 m and x = 2 m.
  • #1
Chan M

Homework Statement


1. [/B]The only force acting on a 4.0 kg body as it moves along the x-axis varies as shown in the figure. The velocity of the body at x = 0 is 7.0 m/s.
c) What is the maximum kinetic energy attained by the body between x = 0 and x = 8 m?
upload_2017-10-10_19-24-29.png

Homework Equations


Work = delta K
K = kinetic energy
K = 0.5 * m * v^2
v = velocity
m = mass
Work is integral of the function of Force in regards to position

The Attempt at a Solution


So in looking at the graph, 0-1 meters, K has a positive change of 2.5 J. Between 1-2 meters, K has a negative change of 2.5 J. So they cancel out, v at 0 meters equals v at 2 meters, which is 7 m/s

Also, initial kinetic energy is 98 J
98 J = 0.5 * 4kg * (7 m/s)^2
Thus, we can find the kinetic energy at 8 meters by subtracting 2 meters and starting at the 2 meter mark since K at 2 meters equals K at 0 meters because velocities are the same at these points.

And because F is constant between 2 and 8 meters, we can simply use the W = Fd equation.
So that...
F * dr = K - Ko
-5N * 6m = K - 98J
K = 68 J

I know this isn't the correct answer, I don't know why and I need to know how to get to the correct answer.

Thanks!
 
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  • #2
Hello Chan ,

You are required to find maximum kinetic energy .Does this happen at x = 8m ?
 
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  • #3
conscience said:
Hello Chan ,

You are required to find maximum kinetic energy .Does this happen at x = 8m ?

Well the energy starts out at 98J, goes up then goes back down and returns to 98J at 2 meters. The kinetic energy then decreases as the velocity decreases due to the negative force. The maximum Kinetic energy is said to be over 100J but I can't see how this is possible in any way.
 
  • #4
I just solved the problem, thanks.
 

Related to Question Regarding Changes in Kinetic Energy

1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion.

2. How is kinetic energy calculated?

Kinetic energy is calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

3. What factors affect the changes in kinetic energy?

The factors that affect the changes in kinetic energy include the mass and velocity of the object, as well as any external forces acting on the object.

4. How does kinetic energy relate to potential energy?

Kinetic energy and potential energy are two forms of energy that are interrelated. As an object moves, its potential energy decreases while its kinetic energy increases.

5. Can kinetic energy be converted into other forms of energy?

Yes, kinetic energy can be converted into other forms of energy, such as thermal energy, sound energy, or electrical energy, depending on the situation.

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