Answer to Question #155981 in Physics for Duc

Question

A crate of mass 10kg is pulled up a rough incline with an initial speed of 1.5m/s. The pulling force is 100N parallel to the incline, which makes an angle of 20° with the horizontal. The coefficient of kinetic friction is 0.4, and the crate is pulled 5m. (a) How much work is done by the gravitational force on the crate? (b) Determine the increase in internal energy of the crate-incline system owing to friction. (c) How much work is done by the 100N force on the crate? (d) What is the change in kinetic energy of the crate? (e) What is the speed of the crate after being pulled 5m?

Answer 1

(a)

$W=F_g\cdot h\cdot\cos180°=mg\cdot s\cdot \sin20°\cdot\cos180°=$

$=10\cdot9.8\cdot 5\cdot \sin20°\cdot\cos180°\approx-168(J)$ .Answer

(b)

$Q=F_f\cdot s\cdot\cos180°=\mu\cdot mg\cdot\cos20°\cdot s\cdot\cos180°=$

$=0.4\cdot 10\cdot 9.8\cdot\cos20°\cdot 5\cdot(-1)=-184(J)$ .Answer

(c)

$W=F\cdot s=100\cdot5=500(J)$ .Answer

(d)

$\Delta KE=\sum{W_i}=500-168-184=148(J)$ .Answer

(e)

$\frac{mv_f^2}{2}-\frac{mv_0^2}{2}=\Delta KE\to v_f=\sqrt{\frac{2\cdot\Delta KE}{m}+v_0^2}=$

$=\sqrt{\frac{2\cdot148}{10}+1.5^2}=5.649(m/s)$ .Answer