1) A 2.0-kg box is sitting on a ramp inclined at an angle of 20 degrees. It is currently stationary. The coefficient of static friction between the ramp and the box is 0.58, and the coefficient of kinetic friction is 0.30. (16 points)

a) Draw a free-body diagram of the box complete with labels, axes, and angles. Indicate, which forces cancel out, if any.

b) What is the acceleration of the box?

c) What is the magnitude of the frictional force?

d) What is the largest angle that the ramp can be tilted before the box begins to move? Start from Newton's Second Law to show your answer.

2) An 80-kg Astronaut is training for arriving on a newly discovered planet, Planet X. This new planet has the same radius of earth but double the mass of earth.

While training on Earth, the astronaut wants to simulate his gravitational weight on Planet X by wearing a weighted vest. How many extra kilograms does he need to wear in order to simulate his weight on Planet X? (G= 6.6710^-11 N*m? /kg?, M_Earth=5.9710²⁴kg, R_Earth =6.36x10⁶m).

3) Two packages are connected by a very light string that goes over an ideal pulley as shown in the figure. The 10 kg package sits on a rough surface while the 6.3 kg mass hangs over. Once the 6.3 kg mass is released, each block moves a distance of 35 cm in 0.82 seconds