Question

A 5.7 kg particle starts from rest at x = 0 and moves under the influence of a single force Fx = 4.5 + 13.7 x − 1.5 x 2 , where Fx is in Newtons and x is in meters. Find the work done by this force on the particle as the particle moves from x = 0 m to x = 1.9 m. Answer in units of J.

Answer 1

Answer:

The work done by the force on the particle is 29.85 J.

Explanation:

The work is given by:  

$W = ^{x_{2}}_{x_{1}}\int F_{x} dx$

Where:

x₁: is the lower limit = 0 m    

x₂: is the upper limit = 1.9 m

Fₓ: is the force in the horizontal direction =  (4.5 + 13.7x - 1.5x²)N

$W = ^{1.9}_{0}\int (4.5 + 13.7x - 1.5x^{2}) dx$  

$W = 4.5x|^{1.9}_{0} + \frac{13.7}{2}x^{2}|^{1.9}_{0} - \frac{1.5}{3}x^{3}|^{1.9}_{0}$  

$W = 4.5N(1.9 m) + \frac{13.7N}{2}(1.9 m)^{2} - \frac{1.5N}{3}(1.9 m)^{3}$    

$W = 4.5N(1.9 m) + \frac{13.7N}{2}(1.9 m)^{2} - \frac{1.5N}{3}(1.9 m)^{3}$      

$W = 29.85 J$

Therefore, the work done by the force on the particle is 29.85 J.

I hope it helps you!