Practice

$1996$M$2.$ A $300-kg$ box rests on a platform attached to a forklift, shown above. Starting from rest at time $=0,$ the box is lowered with a downward acceleration of $1\mathrm{.}5\frac{m}{s^2}$

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

At time $t=0,$ the forklift also begins to move forward with an acceleration of $2\frac{m}{s^2}$ while lowering the box as described above. The box does not slip or tip over.

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

c$.$ Given that the box does not slip, determine the minimum possible coefficient of friction between the box and the platform.

d$.$ Determine an equation for the path of the box that expresses $y$ as a function of $x($and not of $t),$ assuming that, at time $t=0,$ the box has a horizontal position $x=0$ and a vertical position $y=2m$ above the ground, with zero velocity.

e$.$ On the axes below sketch the path taken by the box