as the force required before you changed the crate’s orientation. You are pushing a wooden crate across the floor at constant speed. You decide to turn the crate on end, reducing by half the surface area in contact with the floor. In the new orientation, to push the same crate across the same floor with the same speed, the force that you apply must be about 1. four times as great 2. twice as great 3. equally great 4. half as great 5. one-fourth as great as the force required before you changed the crate’s orientation. The frictional force does not depend on surface contact area! Answer: 3.The force is proportional to the coefficient of kinetic friction and the weight of the crate. Neither depends on the size of the surface in contact with the floor.

An object is held in place by friction on an inclined surface An object is held in place by friction on an inclined surface. The angle of inclination is increased until the object starts moving. If the surface is kept at this angle, the object 1. slows down. 2. moves at uniform speed. 3. speeds up. 4. none of the above Answer: 3. As the tilt of the surface is increased at a certain angle the object starts sliding. Until that angle is reached, the object is at rest, and the net force on it is zero. For the object to start sliding from rest, there must be a net force on it; if the net force is no longer zero, the object will accelerate. Net force is no longer zero.

Example: A truck drags a car with locked wheels up a 30o concrete incline. The car has a mass of 1000 kg, the truck pulls with a force of 15 kN and the coefficient of kinetic friction between rubber and concrete is 0.8. What is the frictional force acting on the car? What is the acceleration of the car? a) N F fk W b)

Circular Motion: We know that a an object traveling in a circular path has a centripetal (center seeking) acceleration directed towards the center of curvature. Where does this acceleration come from? If there is an acceleration it must be due to a net force in the same direction as the acceleration. This net force that causes a centripetal acceleration is called a centripetal force. The centripetal force is not a specific force, it is any force that causes an object to accelerate towards the center of curvature. Examples: The planets move in (roughly) circular orbits, what is the centripetal force keeping the planets in orbit? Gravitational force directed towards the large central mass. A mass attached to a string is swung in a circle over a person’s head. What is the centripetal force keeping the mass in its circular path? The tension in the string pulls the mass towards the center. A car driving around a curve is traveling in part of a circular path. What keeps the car in this circular path? Friction between the tires and the road directed towards the center of the curve.

Example: What is the max speed a car can go around a 20o banked curve without sliding? The curve has a radius of 10 m and the static coefficient of friction between the tires and the road is 0.8. z N r 20o fs W The max velocity depends on the incline angle and the radius of curvature.