Answer to Question #260292 in Mechanics | Relativity for Pranali

Question

A 3.0 kg block is acted upon by a variable horizontal force F(x) = 24.0−9.0x, where the force is in newtons if x is measured in meters. The coefficient of kinetic friction between the block and the flat surface is 0.19. The block is initially at x = 0 m. What distance must the block travel if the net work done on the block by F(x) and friction combined is to be exactly zero?

At what point along the way does the net force on the block reach zero?

Answer 1

$m = 3.0kg$

$\mu = 0.19$

$g \approx10\frac{m}{s^2}$

$x_0 = 0$

$F = 24.0-9.0x$

$F_{fr} =\mu mg$

$W_{fr}= - F_{fr}*(x-x_0)= - \mu mgx=-5.7x$

$W_f =\smallint^x _0F(x)dx= 24x -4.5x^2|^x_0=24x-4.5x^2$

$W =W_f+W_{fr}= -5.7x+24x-4.5x^2$

$18.3x-4.5x^2= 0$

$x_1 =0; x_2 \approx 4.01$

$\text{Answer: }4.01 m$