What is the least amount of time in which this motion can be completed without the top block sliding on the lo

Question

The coefficient of static friction is 0.60 between the two blocks in figure. The coefficient of kinetic friction between the lower block and the floor is 0.20. Force F_vec causes both blocks to cross a distance of 5.0 m, starting from rest.

Answer 1

this question does not provide enough info to solve problem

you need at to know the mass of both blocks

this is because the force static friction only depends on the weight of the top block NOT the bottom block

And the force of kinetic friction depends on the weight of both blocks or the entire system

the answer of 1.3 seconds (Adam F) assumed that the weight of both blocks is taken into consideration when calculating the static friction force which is not true since only the the weight of the top block is required the bottom block has no influence on static friction between it and top block; the normal force is only weight of top block

hope this helps

Answer 2

Max acceleration of the top block is 0.60 g  since that is the maximum force of friction divided by the mass of the block .

so here we go.

0.5  a * t^2 =5

0.5 * 0.6 g *t^2 =5

t^2 = 5 / (0.5 * 0.6 * g)

t = SQRT( 5 / (0.5 * 0.6 *g )) = 1.29 seconds  if g = 10 m/s/s

or with g = 9.8 m/s/s  then t = 1.30 seconds