5.1 Forces in 2-D; Vectors

5.1 Summary

• When two vectors are at right angles, you can use the Pythagorean theorem to determine the magnitude of the resultant vector

• The law of cosines and the law of sines can be used to find the magnitude of the resultant of any two vectors

• The components of a vector are projections of the component vectors

• Vectors can be summed by separately adding the x- and y-components

5.2 Friction

Weight

• Fg: is the vector quantity directed toward the center of Earth (called: weight)

• When mass and acceleration of gravity are known weight can be calculated

• Fg = mg

The Normal Force

• A television is on a table: why doesn’t the TV continue to fall to the center of the earth

• The TV is in equilibrium (not moving), the TV has Fg, therefore it has a normal force (Fn) (in the opposite direction that is equal to Fg)

Force Normal

• Use “normal” because the direction of the contact force is perpendicular to the table surface

• “normal” means perpendicular

• Normal force is always perpendicular to the contact surface

Force of Friction

• Friction opposes the applied force• Static friction (Fs) the resistive force that keeps the jug

from moving

• As long as the jug does not move, Fs = -Fapplied

• When the applied force is as great as it can be without causing the jug to move it has reached its maximum Fs,max

Force of Friction

• When the applied force on the jug exceeds Fs,max, the object moves.

• There is still a frictional force acting on the object as it moves, but it is less than Fs,max

• Kinetic friction (Fk) the resistive force that opposes the two contacting surfaces that are moving past one another

Force of Friction

• When two surfaces are stationary with respect to each other, the surfaces stick together somewhat at the contact points

• Adhesion is caused by electrostatic forces between molecules of the two surfaces

• Due to adhesion, the force required to cause a stationary object to begin moving is usually greater than what is necessary to keep it moving.

Demo 1: Static vs. Kinetic Friction

• Is Kinetic friction less than static friction?

• Procedure: Use the spring scale to measure the force required to start the rectangular block moving. Then use the spring scale to measure the frictional force for constant velocity. Perform several trials. Have students record all data and find the average for each. (note: normal force and the surfaces remain the same, the only difference in the two average values is due to motion)

Demo 2: Static vs. Kinetic Friction

• Does friction depend on the surface?

• Procedure: attach the hook to one of the two uncovered sides of the block. Pull the block across the table with the spring scale. Repeat the demo. With each new surface of the cube exposed to the table. Repeat with a different cube and different surfaces (glass, carpeting, sandpaper) Summarize results and reach a conclusion

Coefficient of friction

• Coefficient of friction: the ratio between the normal force and the force of friction between two surfaces.

• Coefficient of friction: the ratio of the force of kinetic friction to the normal force.