Question

six crates(a,b,c,d,e,f) at rest on level surfaces. The crates have differentmasses and the frictional coefficients [given as $(\mu_{\rm s},\mu_{\rm k})$ ] between the crates and the surfaces differ. Thesame external force is applied to each crate, but none of thecrates move.

Rank the crates on the basis of thefrictional force acting on them.

Rank from largest to smallest.

a. [500kg  μ=(0.6,0.3)]      b. [750kg μ=(0.4,0.3) ]      

c. [250kg  μ=(0.2,0.1)]       d.[600kg μ=(0.8,0.5)]         

e.[750kg  μ=(0.6,0.5)]       f. [1500kg μ=(0.3,0.1) ]

                 

Answer 1

This is a trick question. It says the same external force isapplied to each crate, but none of them move. This means that foreach crate, a static friction force opposes the motion. The staticfriction force acts opposite the horizontal component ofthe applied external force. And the static friction force, for eachcrate, must be equal to (and opposite of) this horizontal appliedforce, so that in each case the total horiz force is zero.

Therefore, since eachcrate has the same applied force, all six crates have the samestatic friction force acting on them! The static frictionforce is NOT the coeff times the normal! It is only theamount of static friction necessary to keep the object from moving.So in this case, all six have the same static friction force.

Answer 2

The point is that if a crate doesn't move than the externalforce acting on it is balanced by the friction force. Since nocrates moved we conlude that all friction forces are the same(equal to the unique external).

Friction force of sliding (it depends only on μ andweight of the body) is different from friction force at rest(which changes with the external force until some limit, whenthe body finally starts to slide).

So, the answer is: all the same, a=b=c=d=e=f.