For what value of x will this object first come to rest?

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In summary, the problem discusses a 2.0-kg object moving along the x-axis at 5.0 m/s with a force of (-4.0x) N acting on it. The objective is to find the value of x at which the object first comes to rest. Using the equations for kinetic energy and work, an initial attempt at solving the problem leads to an incorrect answer of 2.5m. However, after considering the changing force with distance and integrating to find the total work, the correct answer of 3.5m is obtained. This highlights the importance of considering the changing force when calculating the work done by it.
  • #1
gijungkim
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Homework Statement


A 2.0-kg body moving along the x-axis has a velocity vx = 5.0 m/s at x = 0. The only force acting on the object is given by Fx = (–4.0x) N, where x is in m. For what value of x will this object first come (momentarily) to rest?

Homework Equations


0.5 mv^2 = KE
F*d = work

The Attempt at a Solution


Since KE = 0.5 * 2 * 5^2 = 25J
and F*d = -4.0x^2
-4x^2 = 25J
x = 2.5 m
This is how I approached it, but the answer is 3.5m. Can anyone help me out?
 
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  • #2
Since the force changes with x, what will be the work done by the force when the body moves by a distance dx?
Integrate it to find the total work and the expression you get comes out to be different. why?
you can't find the net work done like this:
gijungkim said:
and F*d = -4.0x^2
everything else is correct. Just the left hand side of the equation.
 
  • #3
AdityaDev said:
Since the force changes with x, what will be the work done by the force when the body moves by a distance dx?
Integrate it to find the total work and the expression you get comes out to be different. why?
you can't find the net work done like this:

everything else is correct. Just the left hand side of the equation.
Oh I got it now
Fxdx = -4.0x dx
W = -2.0x^2 J = 0.5 * 2 * 5^2 J
x = 3.5m right??
Thank you so much!
 
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  • #4
The force changes as the position of particle changes. So you can't get the value of work done by simply multiplying F with x.
 
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  • #5
AdityaDev said:
The force changes as the position of particle changes. So you can't get the value of work done by simply multiplying F with x.
Got it now! Thank you for helping me!
 

Related to For what value of x will this object first come to rest?

1. What does it mean for an object to come to rest?

When an object comes to rest, it means that it has stopped moving and is no longer in motion. This can occur when the forces acting on the object are balanced, resulting in a net force of zero.

2. How is the value of x related to an object coming to rest?

The value of x is often used to represent time in equations related to an object's motion. For an object to come to rest, the value of x would represent the amount of time it takes for the object to stop moving.

3. Why is it important to know the value of x for an object to come to rest?

Knowing the value of x can help us understand the motion of an object and predict when it will come to rest. It can also be used to calculate other factors such as velocity and acceleration.

4. How can we determine the value of x for an object to come to rest?

The value of x can be determined by using equations of motion, such as the equation for average velocity (x = vt) or the equation for displacement (x = 0.5at^2), where v is velocity, t is time, and a is acceleration. By plugging in known values, we can solve for x.

5. Are there any factors that can affect the value of x for an object to come to rest?

Yes, there are multiple factors that can affect the value of x. Some of these factors include the initial velocity of the object, the direction and magnitude of the forces acting on the object, and the surface on which the object is moving. Additionally, air resistance and other external factors can also impact the value of x.

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