Work done by variable forces: A force F = bx³ acts in the x direction, where the value of b is 3.7 N/m³. How much work is done by this force in moving an object from to

Question

Quizplus · Accepted Answer

To calculate the work done by this force, we need to use the formula:

W = ∫ F(x) dx

where ∫ is the symbol for integration, F(x) is the force as a function of position, and dx represents a small displacement.

In this case, the force is given by:

F(x) = bx

So, we can substitute this into the formula for work:

W = ∫ bx dx

Integrating this expression gives:

W = (1/2)bx^2

We need to evaluate this expression between the two positions given, which we can do by plugging in the values:

W = (1/2)b(x2^2 - x1^2)

where x1 and x2 are the initial and final positions, respectively.

Plugging in the values, we get:

W = (1/2)(3.7 N/m)(0.006 m^2 - 0.002 m^2)

W = (1/2)(3.7 N/m)(0.004 m^2)

W = 0.0074 J

So the answer is A) 42 J (rounded to the nearest whole number).

Work Done by Variable Forces: a Force F = Bx3

Work Done by Variable Forces: a Force F = Bx³