Answer to Question #257809 in Mechanics | Relativity for denys

Question

A crate of mass 10.0 kg is pulled up a rough incline with an initial speed of 1.50 m/s. The

pulling force is 100 N parallel to the incline, which makes an angle of 20.0° with the

horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 5.00 m.

(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 due to friction. (c) How much work is

done by the 100-N 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 5.00 m?

Answer 1

a)

$A=mgh=mgl\sin20°=168~J,$

b)

$U=F_{fr}l=\mu mgl\cos 20°=184~J,$

c)

$A'=(F-\mu mg\cos 20°)l+mgl\sin 20°=483~J,$

d)

$\Delta E=A'-\frac{mv^2}2=472~J,$

$u=\sqrt{\frac{2\Delta E}m}=9.7~\frac ms.$