Your Assignment:
1) Execute Problem 1. 
   (Do not execute Problem 2 until you fill in the blanks.)
2) I have done problem #1 
3) You hand in  problem #2

Problem 1:

You are given a mass M=15Kg, on an incline of 35 degrees, and there is an external force F=40N.  Find the normal force N, and the acceleration along the incline.

Newton's 2nd law along the incline gives equation 1 (eq1):
(Note the difference of = and == )

Clear["Global`*"];

eq1=  m g Sin[theta] - F == m ax

Newton's 2nd law perpendicular to the incline gives equation 2 (eq2):

eq2= N - m g Cos[theta] == 0

We Solve eq1 and eq2 for N and ax. We Simplify the solution.

sol= Solve[{eq1,eq2},{N,ax}] //Simplify

Finally, we plug in the values given in the problem.

sol //.{g->10, m->15, theta-> 35 Degree, F->40} //N

Quiz 4: Problem 2:
You need to fill in the equations!!!

You are given two blocks of mass m1=10 and m2=10 on an incline of angel theta=35 degrees. Find the normal force N, the tension T, the acceleration of block one a1x, and the acceleration of block two a2y.  (Hint: note a1x == a2y)

Newton's 2nd law along the incline gives equation 1:

Clear["Global`*"];

eq1=  m1 g Sin[theta] - T == m1 a1x

Newton's 2nd law perpendicular to the incline gives equation 2:
(You fill in something.)

eq2=  something == something

Newton's 2nd law for mass 2 gives equation 3:
(You fill in something.)

eq3=  something == something

The relation between a1x and a2y gives equation 4:
(You fill in something.)

eq4=  something == something

We Solve and Simplify the solution.  (Sure beats doing it by hand.)

sol= Solve[{eq1,eq2,eq3,eq4},{N,T,a1x,a2y}] //Simplify

Finally, we plug in the values given in the problem.

sol //.{g->10, m1->10, m2->20, theta-> 35 Degree} //N

Note that the magnitudes of a1x and a2y are equal.