Calculating Final Velocity Using Force-Displacement Graph

In summary, to find the final velocity of a 9.9kg object with an initial velocity of 28.6 m/s at a displacement of 30 meters, you need to calculate the work done by finding the area under the Force v. Displacement graph. The work done is then substituted into the equation W = 1/2mv(final)^2 - 1/2mv(initial)^2, and solved for v(final). The work done in this case is 2500 Joules, and the final velocity is 36.4 m/s.
  • #1
df102015
27
1

Homework Statement


If the following Force v. Displacement graph is for a 9.9kg object and it's initial velocity is 28.6 m/s the what is its velocity at 30 m?
0406768d-b992-4a57-9d87-a50f2b36ebc3.gif


Homework Equations


I am not certain that i am even using the right equations with this but:

W = fd
KE = 1/2mv(final)^2 - 1/2mv(initial)^2

The Attempt at a Solution


I thought since W=Fd and work is proportional to kinetic energy, which is
KE=1/2mv(final)^2 - 1/2mv(initial)^2 and i then could substitute in the Fd, making the new equation:

Fd = 1/2mv(final)^2 - 1/2mv(initial)^2

This could then be rearranged to find final velocity:

sqrt { (Fd + 1/2mv(initial)^2) / 1/2m } = v(final)

Only the issue is that i do not know which F to use to find the final velocity at d=30meters. Because if i use the 0 the whole Fd cancels out, and i get the wrong answer. But if i use 100 then it comes out as larger than the initial velocity, which is not possible as it is losing speed due to lack of force after 20 meters.
 
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  • #2
df102015 said:
If the following Force v. Displacement graph is for a 9.9kg object and it's initial velocity is 28.6 m/s the what is its velocity at 30 m?

Actually work done is a scalar product of force and displacement vector and the amount of work done is sored with the body as kinetic energy so calculate the work done from the graph and use it to find the final velocity.
 
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  • #3
drvrm said:
Actually work done is a scalar product of force and displacement vector and the amount of work done is sored with the body as kinetic energy so calculate the work done from the graph and use it to find the final velocity.

thanks, haha so i was way off, isn't work then supposed to be the area under the line on the graph?
 
  • #4
df102015 said:

Homework Statement


If the following Force v. Displacement graph is for a 9.9kg object and it's initial velocity is 28.6 m/s the what is its velocity at 30 m?
0406768d-b992-4a57-9d87-a50f2b36ebc3.gif


Homework Equations


I am not certain that i am even using the right equations with this but:

W = fd
KE = 1/2mv(final)^2 - 1/2mv(initial)^2

The Attempt at a Solution


I thought since W=Fd and work is proportional to kinetic energy, which is
KE=1/2mv(final)^2 - 1/2mv(initial)^2 and i then could substitute in the Fd, making the new equation:

Fd = 1/2mv(final)^2 - 1/2mv(initial)^2

This could then be rearranged to find final velocity:

sqrt { (Fd + 1/2mv(initial)^2) / 1/2m } = v(final)

Only the issue is that i do not know which F to use to find the final velocity at d=30meters. Because if i use the 0 the whole Fd cancels out, and i get the wrong answer. But if i use 100 then it comes out as larger than the initial velocity, which is not possible as it is losing speed due to lack of force after 20 meters.

As the force changes over time, The best way to find the work in graphs is by getting the area
KhJXEzh.png


You have a triangle and a rectangle. Find the area and sum it up. You will end you will the the work done
 
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  • #5
df102015 said:
Only the issue is that i do not know which F to use to find the final velocity at d=30meters. Because if i use the 0 the whole Fd cancels out, and i get the wrong answer. But if i use 100 then it comes out as larger than the initial velocity, which is not possible as it is losing speed due to lack of force after 20 meters.

in the graph the value of force and displacement is given so calculate the work done
 
  • #6
Biker said:
As the force changes over time, The best way to find the work in graphs is by getting the area
KhJXEzh.png


You have a triangle and a rectangle. Find the area and sum it up. You will end you will the the work done

And do i use the numbers of the x and y axes to find area? in this case the rectangle being 100x20 and the triangle as 1/2x100x10 ?
 
  • #7
i keep getting an answer larger than the initial velocity of 28.6, is that at all possible?
 
  • #8
Biker said:
As the force changes over time, The best way to find the work in graphs is by getting the area
KhJXEzh.png


You have a triangle and a rectangle. Find the area and sum it up. You will end you will the the work done

I got 2500 for the work, is that correct?
 
  • #9
I haven't calculated the velocity but it should be larger than the initial. Work is adding energy to the system. You add more energy this energy will be kinetic. While the mass and 0.5 obviously don't change then the only thing that will change is the velocity.

and the work is 2500 right :D

So yes it should be larger.
 
  • #10
df102015 said:
I got 2500 for the work, is that correct?
Yes. So, show us your detailed calculations for getting the final velocity. Incidentally, what are the units.
 
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  • #11
Chestermiller said:
Yes. So, show us your detailed calculations for getting the final velocity. Incidentally, what are the units.

W = 1/2mv(final)^2 - 1/2mv(initial)^2
2500 = (0.5 x 9.9 x V^2) - (0.5 x 9.9 x 28.6^2)
2500 = 4.95V^2 - 4048.9
6548.9 = 4.95V^2
1323.0 = V^2
36.4 = v(final)

Units:
W is in Joules
Mass is in kilograms
Velocity is in meters per second
Displacement is in meters
Force is in Newtons
 
  • #12
I didn't check your arithmetic, but your approach looks OK.
 
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  • #13
Chestermiller said:
I didn't check your arithmetic, but your approach looks OK.

Thank you, i got the right answer, just checked it! (:
 
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FAQ: Calculating Final Velocity Using Force-Displacement Graph

What is a "Force v Displacement graph"?

A "Force v Displacement graph" is a graphical representation of the relationship between the applied force on an object and the resulting displacement. It shows how the force applied to an object affects its position or movement.

How is a "Force v Displacement graph" created?

A "Force v Displacement graph" is created by plotting the applied force on the x-axis and the resulting displacement on the y-axis. The data points are then connected to form a line, which can help visualize the relationship between force and displacement.

What does the slope of a "Force v Displacement graph" represent?

The slope of a "Force v Displacement graph" represents the stiffness or rigidity of the object. A steeper slope indicates a higher stiffness, meaning that it takes more force to cause a certain amount of displacement. A flatter slope indicates a lower stiffness, meaning that less force is needed to cause the same amount of displacement.

What can a "Force v Displacement graph" tell us about an object?

A "Force v Displacement graph" can tell us about the mechanical properties of an object, such as its stiffness and the amount of force needed to cause a certain displacement. It can also show if an object follows Hooke's law, which states that the force applied to an object is directly proportional to the resulting displacement.

How can a "Force v Displacement graph" be used in scientific research?

A "Force v Displacement graph" can be used in scientific research to study the behavior of materials and objects under different forces. It can also be used to compare the properties of different materials and to understand how they respond to external forces. In engineering, it can help in designing and testing structures to ensure they can withstand the necessary forces without breaking or deforming.

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