A force of 8 N acts on a 2 kg object as it is displaced along the x-axis. The speed of the object when it is at x= 2m is 5 m/s.
a) what is the net work done by F(x) on the object as it is displaced from x=2m to x=8m?
sol) 8m - 2m = 6m; 6m * 8N = 48 J
b) What is the object's kinetic energy at x= 8m?
sol) Kf= Ki - W(net)
= 25J + 48 J
= 73 J (a bit too much ??)
c) what is the instantaneous power delivered by Fx when the object is at x=8m?
sol) P = F * v
= 8N * 73m/5 (?)
(a) correct
(b) E = (1/2) M V^2 + Work = 25 J + 48 = 73 J. Correct
V = sqrt(2E/m) = 8.54 m/s
(c) F*V = 8N * 8.54 m/s = 63.4 W
(Friction has been assumed negligible)
(a) The net work done by F(x) on the object as it is displaced from x=2m to x=8m can be calculated by multiplying the force (8 N) by the displacement (6 m). So, the net work done is 8 N * 6 m = 48 J.
(b) To calculate the object's kinetic energy at x=8m, we can use the equation Kf = Ki - W(net), where Kf is the final kinetic energy, Ki is the initial kinetic energy, and W(net) is the net work done. Given that the initial kinetic energy is 25 J (given in the question), we can substitute the values into the equation: Kf = 25 J - 48 J = -23 J. However, it seems that there might be an error in the calculation since kinetic energy cannot be negative. Double-check the calculations.
(c) The instantaneous power delivered by Fx when the object is at x=8m can be calculated using the equation P = F * v, where P is power, F is force, and v is velocity. Given that the force is 8 N and the velocity is 5 m/s (given in the question), we can substitute these values into the equation: P = 8 N * 5 m/s = 40 W.