Here is the Problem: As shown in the diagram, a block of mass m on ahorizontal f

Question

Here is the Problem:

As shown in the diagram, a block of mass m on ahorizontal floor is pulled along the floor by a cord that exerts aforce of magnitude F at an angle q above thehorizontal. The coefficient of kinetic friction between theblock and the floor is muK(where mu here should be theGreek symbol mu, see figure below).

A) Derive an expression for the magnitude of the accelerationa of the block.

B) Derive an expression for the speed of the block a time "Deltat" after it starts moving (where Delta should be the Greek symbolDelta).

Be sure your derivation of the answer clearly contains the threesteps described in lecture: (1) Free-body diagram, (2) choice ofcoordinate systems, and finally (3) equationsFx=max, Fy=may.

An algebraic formula, as opposed to a numerical answer, is onewhich contains symbols (such as m1 or g) instead ofnumbers with units (such as 9.8 m/s2).  Dimensionless numbers such as p or ½ are perfectly OK in analgebraic formula, but numbers with dimensions are not allowed.

Explanation / Answer

Taking the horizontal forces we have as, Fcos-fr=ma fr=kN=kmg frictionalforce Here a is the resultant acceleration produced. Fcos-kmg=ma a=(Fcos-kmg)/m v=u+at u=0 initial velocity t=time taken v=final velocity after time t v=(Fcos-kmg)/m*t Hence we get by it.

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