What is the cause behind different friction coefficient values? The description of friction we have been using is empirical; it's not based on a detailed microscopic model. The details of the interactions between the molecules making up the surfaces in question lead to the different coefficients of friction. In this connction, an interesting question would be to ask you to design an experiment you can perform in an introductory lab that would determine a coefficient of static or kinetic friction.
A skier skies down a slope with angle θ with no friction, starting from rest. She travels a distance d1. and falls. After the fall, there is friction, with coefficient μk . What is the distance d1 she will slide before coming to a stop?
A fish tugs on a line with some force causing tension on the line. The pole is at a specific angle in the air. It's hard to make a question I like out of this one.
Why is friction related to the normal force? Good question. It again has to do with the microscopic details of friction that our simple empirical model does not account for.
Roller coaster and spit problem. If you're on a roller coaster that is falling down a verical track, and you spit in the air, it doesn't fall on you but appears to hover as you fall. Explain why this is so. To make it more interesting, also explain how friction and air resistance enters the picture.
Projectile motion problem. Quarterback throwing angle, velocity, distance, possible defender?
Attach a string to an object resting on a horizontal surface with friction; coeffients μk and μs. Increase the tension T in the string until the object just begins to move. What will the acceleration be?
Your arm goes in a circular arc as you throw a pie toward the face of a clown. Describe the forces on the pie during this motion, and draw a diagram showing the total force on the pie.