$1.$ If a $360$ kg box is sitting on a flat surface and a force of $1000$N is applied in the x direction and the coefficient of static friction is $\mathrm{.}25,$ will the box move?

a$.$ If the coefficient of kinetic friction is $\mathrm{.}12$ what will be the resulting net acceleration on the box? $($free$-$body diagram and force equations required.$)$

$2.$ If a $1250$N force acts on a $70$kg box in a Northerly direction and a $830$N force acts on the box at an angle of $120$ what is the resultant force on the box?

b$.$ What is the net acceleration of the box?

$3.$ If a $170$kg parachutist jumps out of an airplane what force must the parachute apply to reduce their net acceleration to $-\mathrm{.}5$m$/$s$?$

b$.$ What force must the parachute apply to halt all acceleration?

$4.$ If you apply $1200$N of force on a $250$kg box with a coefficient of static friction of $\mathrm{.}3,$ will the box move?

c$.$ Assume that static friction is overcome and the coefficient of kinetic friction is $\mathrm{.}11,$ what is the net acceleration on the box?

d$.$ What is the box$$s velocity after $45$s$?$

e$.$ How far did the box travel in that time?

$5.$ If your mass on the Earth is $185$kg$,$ what is your mass on the moon?

$6.$ If a $\mathrm{.}5$kg toy car is rolling down a $30-$degree incline:

a$.$ What is the car$$s acceleration in the x$$ direction?

b$.$ If the car sat at the top of the ramp at a height of $4$m$,$ what distance does the car travel down the ramp to the bottom?

c$.$ What is the car$$s final velocity at the bottom of the ramp?

d$.$ What is the free$-$body diagram?

e$.$ What force was applied on the car?

$7.$ If a skier starts from rest and slides down a $10000$m long hill at an angle of $30$ degrees to the horizontal:

a$.$ What is the skier$$s acceleration?

b$.$ What is the skier$$s final velocity?

c$.$ How high was the skier when they started down the hill?

$8.$ If the free$-$body diagram of an elevator looks like the following what is happening with the elevator: $($assume everything is completely vertical$)$