A force Fx acts on a particle. The force is related to the position of the particle by the formula Fx = (5.9 N/m3) x3.
Find the work done by this force on the
particle as the particle moves from x = 0.9 m to x = 22 m.
Answer in units of J
To find the work done by a force, you need to integrate the force over the distance traveled. In this case, the force is given by Fx = (5.9 N/m^3) x^3.
The work done, W, can be calculated using the equation:
W = ∫ Fx dx
Integrating the force with respect to x gives us:
W = ∫ (5.9 N/m^3) x^3 dx
To solve this integral, you can use the power rule of integration:
∫ x^n dx = (1/(n+1)) * x^(n+1) + C
Applying the power rule, we have:
W = (5.9 N/m^3) * (1/4) * x^4 + C
Now, to evaluate the definite integral, we substitute the upper and lower limits of x:
W = (5.9 N/m^3) * (1/4) * (22^4 - 0.9^4)
W = (5.9 N/m^3) * (1/4) * (23455 - 0.00068)
W = (5.9 N/m^3) * (1/4) * 23455
W = 34548.0625 Nm
Finally, since work is measured in joules (J), we need to convert the units from N*m to J:
1 J = 1 N*m
Therefore, the work done by the force as the particle moves from x = 0.9 m to x = 22 m is approximately 34548.0625 J.