PROBLEMS FOR CHAPTERS $5-6($Assume $g=10\frac{m}{s^2}$ wherever needed$).$

$1-$ If $M=2\mathrm{.}0kg,$ what is the tension in string $1?$

$2-$ The horizontal surface on which the block slides is frictionless. If $F=20N$ and $M=5\mathrm{.}0kg,$ what is the magnitude of the resulting acceleration of the block?

$3.$ If the only forces acting on a $2\mathrm{.}0-$kg mass are vec$(F{)}_1=(3$hat$(i)-8$hat$(j))N$ and vec$(F{)}_2=(5$hat$(i)+3$hat$(j))N,$ what is the acceleration of the mass?

$4.$ Two blocks, $M_1=2kg,M_2=3kg$ attached to the ceiling of an elevator are accelerating up with $a=0\mathrm{.}4\frac{m}{s^2}.$ Find tensions $T_1$ and $T_2.$

$5.$ A $2-kg$ mass has an acceleration of $(4\mathrm{.}0$hat$(i)+3\mathrm{.}0$hat$(j))\frac{m}{s^2}.$ Only two forces act on the mass. If one of the forces is $(2\mathrm{.}0$hat$(i)-3$hat$(j))N,$ what is the magnitude of the other force

$6.$ A block is pushed across a horizontal surface by the force shown. If the coefficient of kinetic friction between the block and the surface is $0\mathrm{.}20,F=20N,=37,$ and $M=4\mathrm{.}0kg,$ what is the magnitude of the acceleration of the block?

$7.$ A block, $M=5kg$ is released from top of a frictionless inclined plane making $37$ angle with the horizontal. $($i$)$ Find the acceleration of the block along the incline. $($ii$)$ Find the acceleration of the block if the surface is rough causing a friction force of $0\mathrm{.}8,sin37=0\mathrm{.}6,g=10\frac{m}{s^2}).$

$8.$ The block shown is pulled across the horizontal surface at a constant speed by the force shown. If $M=5\mathrm{.}0kg,F=14N$ and $=37,$ what is the coefficient of kinetic friction between the block and the horizontal surface?

$1$