As we saw in Lesson 12, vectors can be resolved into components along perpendicular axis. This is useful in understanding the motion of an object on an inclined plan. Such an object is acted upon by the force of gravity, friction, and the normal force. The normal force is the force of a table on an object when the object is resting on the table. In addition, a force may be pushing or pulling the object up or down the plane.

To understand this motion, you resolve the force of gravity into components parallel to the plane and perpendicular to the plane.

  1. A 500-Newton trunk is place on an inclined plane that forms an angle of 30 degrees with the horizontal. What are the normal and parallel components of the weight?
  2. A 500 N trunk is placed on an inclined plan that forms an angle of 66 degrees with the horizontal. a) Calculate the values of the normal and parallel components of weight. b) Compare your results with those given above for the same trunk on a 30 degree incline. c) When the angle of the incline increases how do the force components acting on the trunk change?
  3. An automobile weighing 12,000 N is parked on a 36 degree slope. What force tends to cause the auto to roll down the hill? What is the support force between the auto and the hill?
  4. A box rests on a plank that is inclined to the horizontal. As the angle between the plank and the horizontal increases, the component of the weight of the box parallel to the plank increases, decreases or remains the same?
  5. A construction company keeps a wooden crate filled with cement partway up a steel ramp (60° incline). The crate and its contents weight 1200 N and are held in place by a rope attached to a post. The tension in the rope is 750 Newtons. a) Compute the normal force between the incline and the crate. b) Compute the amount of frictional force which helps to keep the crate from sliding down the ramp.