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The force applied on a moving object with a mass of #7 kg # on a linear path is given by #F(x)=x #. How much work would it take to move the object over #x in [1,3] #?

Answer 1

Charlotte Aaron

#W = 4# J

The function of force:

#F(x) = x#

Force integrated over a distance equals total work:

#int_1^3F(x)dx#

#=int_1^3xdx#

#=1/2[x^2]_(1)^(3)#

#=1/2(9 - 1) = 4# J

Hence, #W = 4# J.

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Answer 2

Julia Aguilar

To calculate the work done, we use the formula for work: W = ∫ F(x) dx, where F(x) is the force function and the integral is taken over the interval [1,3].

Given F(x) = x, we integrate this function over the interval [1,3]:

∫(1 to 3) x dx = [x^2/2] from 1 to 3 = (3^2/2) - (1^2/2) = (9/2) - (1/2) = 4

Therefore, the work done to move the object over the interval [1,3] is 4 joules.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.