A block of mass is placed on a rough horizontal floor

PHYSICS · Multi-part · AP · Physics C: Mechanics · Force and Translational Dynamics · Force and Translational Dynamics

Problem

A block of mass

m

is placed on a rough horizontal floor. A force

F

is applied to the block by means of a light string making an angle

\theta

above the horizontal. The coefficient of static friction between the block and the floor is

\mu_s

. (Take

g = 9.8\,\text{m/s}^2

.) (i) For impending motion, derive an equation relating

F

\mu_s

m

g

and

\theta

. (ii) Using the result of part (i), obtain an expression for

F

as a function of

\theta

and hence determine the angle

\theta

at which

F

is minimum. (iii) For

m = 10\,\text{kg}

and

\mu_s = 0.50

, calculate the numerical values of the optimum angle and the minimum force.