Freeform

Boxed

$4.$ A $500$ kg box rests on a platform of the electrical fork$-$lift. Starting from rest at time $t=0,$ the box is lowered with a downward acceleration of $1\mathrm{.}4\frac{m}{s^2}.$

a$.$ Determine the upward force exerted by the horizontal platform on the box as it is lowered.

At time $t=0,$ the fork$-$lift also begins to move forward with an acceleration of $1\mathrm{.}9\frac{m}{s^2}$ while lowering the box. The box doesn't slip or tip over.

b$.$ Determine the friction force on the box.

c$.$ If the box doesn't slip, determine the minimum coefficient of static friction between the box and the platform.

d$.$ Determine the expression that describes the path of the box $(y$ as a function of x $),$ assuming, at time $t=0$ the box has a horizontal position $x_0=0$ and a vertical position $y=2\mathrm{.}5m$ above the ground, with zero velocity.

n $n_n$ tho ronrdinate svstem below sketch the path taken by the box.