Applying Newton's second law

1) A cannon shoots a ball at an angle  above the horizontal ground. (a) Neglecting air resistance, use
Newton's Second Law to find the ball's position as a function of time. (Use axes with x measured
horizontally and y vertically.) (b) Let r(t) denote the ball's distance from the cannon. What is the
largest possible value of  if r(t) is to increase throughout the ball's flight? [Hint: Using (a)'s solution
you can write down r^2 as x^2 + y^2, and then find the condition that r^2 is always increasing.]

2) An astronaut in gravity-free space is twirling a mass m on the end of a string of length R in a circle, with
constant velocity w. Write down Newton's second law in polar coordinates and find the tension in the
string.

3) A slab of mass M1 = 40.0 kg rests on a frictionless floor, and a block of mass M2 = 10.0 kg rest on top
of this slab. Between the block and slab, the coefficient of static fraction is 0.60, and 0.40 is the
coefficient of kinetic friction. A horizontal force of 100 N is applied to the block (on top of slab). What
are the resulting accelerations of the block and slab? You must draw pictures and Free Body Diagrams
to get full credit.

4) A student wants to determine the coefficients of static friction and kinetic friction between a box and a
plank. She places a box on the plank and gradually raises one end of the plank. When the angle of
inclination with the horizontal reaches 30°, the box starts to slip, and it then slides 2.5 m down the plank
in 4.0 s at constant acceleration. What are (a) the coefficient of static fraction and (b) the coefficient of
kinetic fraction between the box and the plank? You must draw pictures and Free Body Diagrams to get
full credit.