How much work would it take to horizontally accelerate an object with a mass of 8 kg to 3 m/s on a surface with a kinetic friction coefficient of 6 ?
1 Answer
Explanation:
We're asked to find the necessary work to accelerate an
The equation for work according to the work-energy theorem is given by
ul(W = DeltaE_k = 1/2m(v_2)^2 - 1/2m(v_1)^2
The final velocity is
W = 1/2(8color(white)(l)"kg")(3color(white)(l)"m/s" - 0)^2 = color(red)(ul(36color(white)(l)"J"
However, this does not include the work done to counteract the friction, so we have to use the equation
ul(W = Fs
The necessary force
F = f_k = mu_kmg = (6)(8color(white)(l)"kg")(9.81color(white)(l)"m/s"^2) = 471 "N"
And so we have
W = (471color(white)(l)"N")s
The distance it travels
W_"necessary" = color(blue)(ulbar(|stackrel(" ")(" "36color(white)(l)"J" + (471color(white)(l)"N")s" ")|)