Question

The cube box contains sand and the sand is 520N.

29 The cube box contains sand and weighs 520 N. Try to "roll" the box by pushing the top end of the box horizontally. (A) What is the minimum force required? (b) What is the minimum coefficient of static friction between the box and the floor? (c) If there is a more effective way to roll the box, find the least force. (Gwip: Where does the vertical force act when the box is about to cross over?)

Answer 1

given, weight of sand box is W = 520 N

A. A force F is applied on the top of one side of the cube, and the force F is horizontal
so when the block is about to tip over
the normal reaction of the floor will shift to the edge over which the box is about to tip over
so assuming the side of the cube is a
then From moment balance at the moment of tipping over about the edge over which the block is getting tipped over
From moment balance
F*a = W*a/2
F = W/2
hence minimum force required to tip over the block is 520/2 = 260 N

B. let the coefficient of static friction be u
then
friction force is f
then
From force balance
F = f
and f = uW
hence,
F = uW
u = F/W = 260/520 = 0.5
minimum static coefficient friction required for the block to tip over is 0.5

C. A more effective way to roll the box is to apply force from both sides of the box one on the top side and one on the bottom side