Problems:

1. A bicyclist is coasting down an 8.0° hill at a constant velocity of +8.9 m/s. The mass of the bicycle and rider is 85 kg. A force due to air resistance is directed opposite to the motion and has a magnitude f air. that is proportional to the cyclist's speed v, so that f air = cv, where c is constant. Using the fact that the cyclist is coasting at a constant velocity, determine the numerical value (including units) for the constant c.

2. A skier is pulled up a slope at a constant velocity by a tow bar. The slope is inclined at 25.0° with respect to the horizontal. The fore applied to the skier by the tow bar is parallel to the slope. The skier's mass is 55.0 kg, and the coefficient of kinetic friction between he skis and the snow is 0.120. Find the magnitude of the force that the tow bar exerts on the skier.

3. A 225-kg crate rests on a surface that is inclined above the horizontal at an angle of 20.0°. A horizontal force (magnitude = 535 N and parallel to the ground, not 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?

4. A passenger is pulling on the strap of a 15.0-gk suitcase with a force of 70.0 N. The strap makes an angle o 35.0° above the horizontal. A 37.8-N friction force opposes the motion (horizontal) of the suitcase. Determine the acceleration of the suitcase.

5. A 205-kg log is pulled up a ramp by means of a rope that is parallel to the surface of the ramp. The ramp is inclined at 30.0° with respect to the horizontal. The coefficient of kinetic friction between the log and the ramp is 0.900, and the log has an acceleration of 0.800 m/s². Find the tension in the rope.

6. 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 onto a horizontal path of ice. The coefficient of kinetic friction between the penguin and the ice is the same for the incline as for the horizontal patch. How much time is required for the penguin to slide to a halt after entering the horizontal patch of ice?

7. A toboggan slides down a hill and has a constant velocity. The angle of the hill is 11.3° with respect to the horizontal. What is the coefficient of kinetic friction between the surface of the hill and the toboggan?