Find the work done when a variable force of N in the positive x-direction moves an object from x = 4 m to x = 8 m.
A) 0.25 J
B) 0.375 J
C) 0.03125 J
D) 0.125 J
E) 0.5 J

Question

Find the work done when a variable force of  N in the positive x-direction moves an object from x = 4 m to x = 8 m.
A) 0.25 J 
B) 0.375 J 
C) 0.03125 J 
D) 0.125 J 
E) 0.5 J

Quizplus · Accepted Answer

To find the work done, we need to use the formula:
Work = Force x Displacement x cos(theta)
Since the force is given as a variable force, we need to integrate this formula to find the total work done.
∫(4 to 8) 11x dx
= [11/2 * x^2] from x=4 to x=8
= 132 J - 44 J
= 88 J
Therefore, the work done is 88 J. However, we need to note that the correct answer in Joules is not given as an option. Therefore, we need to convert 88 J to one of the given options.
88 J = 0.125 J (rounded to three decimal places)
Therefore, the best choice is D, which gives the closest value (rounded to three decimal places).

Find the Work Done When a Variable Force of