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1. Find the angle of a supermarket ramp that will alow a person to push a 30 kg shopping cart. The people can push with 50 N of force and friction can be accounted for with a coefficient of 0.10.

For this question I broke up gravity in the x and y direction since it is on a ramp. Fg in y=mgcos(Theta) Fg in x=mgSin(Theta)

My two Fnet equations are:

Up is positive Fnet=Fn-Fgy

0=Fn-Fgy

Fn=mgCos(Theta)

Right is positive Fnet=Fapplied-Ffriction-Fgx

0=50-(0.1)*(30)*(9.8)*cos(Theta)+(30)*(9.8)*sin(Theta)

50=29.4cos(Theta)+294sin(Theta)

And then I dont know what to do next.

2. Block m1 has a mass of 4 kg and block m2 has a mass of 2 kg. The coefficient of friction between m2 and the horizontal surface is 0.50 and the coefficent between m1 nd the inclined surface is 0.289. The incline is 30(degrees). Find the tension in the string and the acceleration of the blocks.

The answer I got is Tension=29.4 N and acceleration is 9.8 m/s^2. Am i right?

3. Your friend has been chained on the wall of a dungeon. You can not get into the room, and the only way to save him is to pull on a rope and drag the 100 kg box with the food and keys on it. Your friend can only reach 1 m and the top of the box is 1 m above the floor and 7 m away from the wall where he is chained. The rope goes through a wall 5 m above the floor. The coefficient of friction between the box and the florr is 0.5. THe rope is old and will break if you pull with more than 550 N. Can you save your friend? If you cannot save him how cloase does the rope get before the rope broke?

Thanks in advance