Question

A. An object of mass m is placed on an inclined plane with a rough surface. Derive an

equation of the acceleration of the object sliding down the incline. [Be sure to

include an appropriate diagram highlighting the relevant forces] (10 marks)

B. A train of mass 200kN has a frictional resistance of 5N per kN. The speed of the

train, at the top of an inclined of 1 in 80 is 45 km/h. Find the speed of the train after

running down the incline for 1km. (10 marks)

Answer 1

A)

$m\vec a=m\vec g+\vec N+\vec F_{fr},$

$ma=mg\sin\alpha-\mu mg\cos\alpha,$

$a=g(\sin\alpha-\mu\cos\alpha),$

B)

$F_{fr}=1~kN,$

$\Delta F=F\sin\alpha-F_{fr}=1.5~kN,$

$a=g\frac{\Delta F}F=0.0735~\frac m{s^2},$

$v_1=\sqrt{v^2-2as}=10.9~\frac {km}h.$