A particle of mass m is subjected to a force acting in the x-direction.

Fx = (3.2 + 0.55x) N.
Find the work done by the force as the particle moves from
x = 0
to
x = 4.5 m.

1

To find the work done by the force as the particle moves from x=0 to x=4.5m, we need to calculate the integral of the force with respect to x.

The work done by a force is given by the equation:

Work = ∫ F dx

In this case, the force Fx = (3.2 + 0.55x) N. To find the work, we integrate this force equation with respect to x:

Work = ∫ (3.2 + 0.55x) dx

To solve this integral, we use the power rule of integration. The integral of a term of the form ax^n is given by (ax^(n+1))/(n+1). Applying this rule, we integrate each term separately:

∫ 3.2 dx = 3.2x

∫ 0.55x dx = (0.55x^2)/2 = 0.275x^2

So, the work done by the force as the particle moves from x=0 to x=4.5m is:

Work = [3.2x + 0.275x^2] evaluated from x=0 to x=4.5

To evaluate this, substitute the upper limit (4.5) and subtract the result when the lower limit (0) is substituted:

Work = [3.2(4.5) + 0.275(4.5)^2] - [3.2(0) + 0.275(0)^2]

Work = [14.4 + 0.275(4.5)^2] - [0]

Work = 14.4 + 0.275(20.25)

Work = 14.4 + 5.56

Work = 19.96 Joules