1) Suppose that the coefficients of static and kinetic friction have values such that µ s =2.0 µ k for a crate in contact with a cement floor. Does this mean that the magnitude of the static friction force acting upon the crate at rest would always be twice the magnitude of the kinetic frictional force acting on the moving crate? Explain your answer.

 2) A 225 Kg. crate rests on a surface which is inclined above the horizontal at an angle 20.0 °. A force (magnitude =535 N and parallel to the incline ) is required to start the crate moving down the incline. What is the coefficient of static friction between the crate and the incline?


 3) A penguin slides at a constant velocity of 1.4 m/s down an icy incline. The incline slopes above the horizontal at an angle of 6.9°. At the bottom of the incline, the penguin slides out onto a horizontal patch of ice. The coefficient of friction between the penguin and the ice is the same for the incline as it is for the horizontal patch. How much time is required for the penguin to slide to a halt after entering the horizontal patch?

 4) A box of bananas weighing 25.0 N rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.40, and the coefficient of kinetic friction is 0.20.

a) If no horizontal force is applied to the box, and the box is at rest, how large is the friction force exerted on the box?

b) What is the magnitude of the friction force if a monkey applies a horizontal force of 7.0 N to the box, and the box is initially at rest?

c) What minimum horizontal force must the monkey apply to the box to start its motion?


 5) A rope is used in a tug-of-war between two teams of five people each. both teams are equally strong so neither team wins. An identical rope is tied to a tree and the same 10 people pull just as hard on the loose end as they did in the contest. In both cases the people pull steadily with no jerking. Which rope if either is more likely to break? Justify your answer.


 6) A 12kg lantern is suspended from the ceiling by two vertical wires. What is the tension in each wire?


 7) During a storm, a limb falls from a tree. It comes to rest across a banded wire fence, one fifth of the way between two fence posts that are 4m apart. the limb exerts a downward force of 151N on the wire, depressing it .2m below the horizontal. Find the tension in the section of wire that is 

a) shorter and b) longer

 8) When a 13.2 kg mass is placed on top of a vertical spring, the spring compresses 5.93 cm.  Find the spring constant of the spring