Question

A box with mass 5kg, at the top of an inclined plane starts to slide down from its initial

resting position. The plane makes an angle of 25° with the horizontal surface.

i. Draw a Free-body diagram for the description above. Make sure it is neat and clear.(5marks)

ii. Derive a fomula for calculating acceleration with respect to the Net force, the frictional force and the force duc to the parallel plane. (3marks)

iii. Calculate thc acceleration (from equation in 'b') of the box if it slides down the plane,assuming a 7N friction force acting on the box due to the surface. (2Marks)

Answer 1

$\text{i.Forces acting on the body:}$

$\vec{F_g}-\text{gravity}$

$\vec N-\text{support normal reaction force}$

$\vec{F_{fr}}-\text{friction force}$

$\text{ii.}\vec F=\vec{F_g}+\vec {F_{fr}}+\vec{N}$

$\vec F=m\vec a$

$\text{Projection of forces on the Y axis:}$

$F_y = 0$

$N-F_g\cos25\degree=0$

$\text{Projection of forces on the X axis:}$

$F_x= F_g\sin25\degree-F_{fr}$

$F = F_g\sin25\degree-F_{fr}$

$a = \frac{ F_g\sin25\degree-F_{fr}}{m}$

$\text{iii.}g=9.81\frac{m}{s^2}$

$F_g = mg = 5*9.81= 49.05N$

$a = \frac{ F_g\sin25\degree-F_{fr}}{m}=\frac{ 49.05*sin25\degree-7}{5}\approx2.75\frac{m}{s^2}$