The Force Vector and Simple Machines

Force is relatively easy to intuit as a vector. The force vector points in the direction in which it is trying to accelerate the object it is acting on.

Since force vectors are so much easier to visualize than acceleration vectors, it is often helpful to first find the direction of the (total) force vector acting on an object, and then use that information to determine the direction of the acceleration vector. Newton's second law, F_total = ma, tells us that the two must be in the same direction.

A component of a force vector.

Pushing a block up a ramp.

→ Solved problem: A cargo plane page 217, problem 9

→ Solved problem: The angle of repose page 218, problem 11

→ Solved problem: A wagon page 218, problem 10

Discussion Questions

A	The figure shows a block being pressed diagonally upward against a wall, causing it to slide up the wall. Analyze the forces involved, including their directions.
B	The figure shows a roller coaster car rolling down and then up under the influence of gravity. Sketch the car's velocity vectors and acceleration vectors. Pick an interesting point in the motion and sketch a set of force vectors acting on the car whose vector sum could have resulted in the right acceleration vector.