Work Question - 4.31 kJ Answer

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In summary, the question asked for the amount of work done by a force with varying applied force on an object moving from 4.56 m to 7.88 m. The correct answer was 4.56692 kJ, which was found by taking the integral of the function and converting it to kJ. The initial attempt resulted in a wrong answer due to a mistake in the given numbers.
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[SOLVED] Work question please help

Homework Statement


An applied force varies with position according to F = k_1x^n − k_2 , where n = 3,
k_1 = 5.6 N/m, and k_2 = 68 N. How much work is done by this force on an object that moves from x_i = 4.56 m to x_f = 7.88 m? Answer in units of kJ.



Homework Equations



Integral from x_i to x_f of the function

The Attempt at a Solution


I attempted to take the integral from 4.56 to 7.99 and got 4310.17 but this is not right. I then thought that I had not converted to kJ so i divided by 1000 and got 4.31017 but that is also wrong. I would appreciate any help.
 
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  • #2
I'm whipping this up on window's calculator, but it doesn't look like you got the right result from integrating

Show your work for the actual integration and we'll make sure you did it right
 
  • #3
Okay...

The antiderivative of 5.6x^3-68 would be 1.4x^4-68x which is then:

=[(1.4(7.99)^4)-(68*7.99)]-[(1.4(4.56)^4)-(68*4.56)]
=5020.973-295.243
=4725.73

Hmm...got a different answer this time...must have done something wrong the first..does this look right now?
 
  • #4
Then to make it into kJ I would just divide by 1000 right?

=4.72573 kJ
 
  • #5
Can I get a confirmation that my work looks correct?
 
  • #6
Yah, as long as you punched in numbers right
 
  • #7
i apologize I made a mistake in the question and put 7.99. It was actually 7.88 like stated at first. I re-integrated and got 4.56692 kJ and this was correct. Thanks for your help.
 

Related to Work Question - 4.31 kJ Answer

What is "Work Question - 4.31 kJ Answer"?

"Work Question - 4.31 kJ Answer" is a measurement of work, specifically 4.31 kilojoules, which is a unit of energy. It is commonly used in scientific calculations and experiments.

How is "Work Question - 4.31 kJ Answer" calculated?

"Work Question - 4.31 kJ Answer" is calculated by multiplying the force applied by the distance over which it is applied. The formula for work is W = Fd, where W is work, F is force, and d is distance.

What is the significance of "4.31 kJ" in "Work Question - 4.31 kJ Answer"?

The value of 4.31 kJ is the amount of energy being used or transferred in the given work scenario. It is a specific and precise measurement that is used to accurately describe the amount of work being done.

How does "Work Question - 4.31 kJ Answer" relate to other units of work?

"Work Question - 4.31 kJ Answer" is equivalent to 4,310 joules (J), which is the SI unit of work. It is also equal to 1.01 calories (cal) or 0.00107 British thermal units (Btu). These units can be converted to and from kilojoules for different purposes.

What are some real-life examples of "Work Question - 4.31 kJ Answer"?

"Work Question - 4.31 kJ Answer" can be seen in various real-life scenarios, such as lifting a 2 kg book 2.155 meters off the ground, pushing a 10 kg box 10 meters across a room, or running up a flight of stairs. It can also be used to measure the work done by machines, such as a car engine or a power drill.

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