Question

A cubical box is filled with sand and weighs 578 N. We wish to "roll" the box by pushing horizontally on one of the upper edges. (a) What minimum force is required? (b) What minimum coefficient of static friction between box and floor is required? (c) If there is a more efficient way to roll the box, find the smallest possible force that would have to be applied directly to the box to roll it. (Hint: At the onset of tipping, where is the normal force located?)

Answer 1

(a)

take torque about right edge where box touches the ground

F * L = W * L/2

F = W / 2

F = 578 / 2

F = 289 N

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(b)

Fnet = ma

Fnet = 0 ( not accelerating)

F - uN = 0

F - uW

u = F / W

u = 0.5

__________________

(c)

what if we applied the force at an angle as below

then

Fcos * L + F sin * L = W * L/2

F ( cos + sin ) = W/2

F = W/2 ( cos + sin )

we need to maximize (cos + sin )

so,

dy / d = -sin + cos = 0

when is sin = cos

= 45 degree

so,

F = 578 / 2 ( cos 45 + sin 45)

F = 204.35 N