Question

A wooden block of mass $M$ resting on a rough horizontal surface is pulled with a force $F$ at an angle with the horizontal. If $\mu$ is the coefficient of kinetic friction between the block and the surface, then acceleration of the block is

• A. $\frac{F}{M}(\cos \phi +\mu \sin \phi )-\mu g$
• B. $F\sin \frac{\phi }{M}$
• C. $\mu F\cos \phi$
• D. $\mu Fsin\,\phi$

Answer 1

Answer: (A)

$\frac{F}{M}(\cos \phi +\mu \sin \phi )-\mu g$

Answer 2

$R=Mg-F\,\sin \phi$ $f=\mu R=\mu =(Mg-F\sin \phi )$ $F=\cos \phi -f=Ma$ $a=\frac{1}{M}[F\cos \phi -f]$ $a=\frac{1}{M}[F\cos \phi -\mu (Mg-F\sin \phi )]$
$=\frac{F}{M}cos\phi -\mu g+\frac{\mu F}{M}\sin \phi$
$=\frac{F}{M}[\cos \phi +\mu \sin \phi ]-\mu g$