Answer to Question #280013 in Mechanics | Relativity for Zizu

Question

.A crate of mass 10kg is pulled up arough incline with an initial speed of 1.5m/s. the pulling force is 100N parallel to the incline which makes an angle of 30° with the horizontal. the coefficient of kinetic friction is 0.4 and the crate is pulled 5m.

a.How much work is done by gravity?

b.how much mechanical energy is lost due to friction?

c.what is the change in kinetic energy of the crate?

d. What is the speed of the crate after being pulled by 5m?

Answer 1

a)

$W= F_g×w×h×cos180°=mg×s×sin20°×cos180°= 10\cdot9.8\cdot 5\cdot \sin20°\cdot\cos180°\approx-168(J)$

b)

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

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

c)

$ΔKE=∑Wi=500−168−184=148(J)$

d)

$\frac{mv_f}{2​}−\frac{mv^2_0}{2}=ΔKE→v_f=\sqrt{\frac{2⋅ΔKE}+v^2_0{m}}=\sqrt{\frac{2\cdot148}{10}+1.5^2}=5.649(m/s)$