5.2 Forces & Equilibrium SOH CAH TOA too

Normal forces If an object is NOT accelerating (at rest or a constant velocity) the net force must be zero. This means that all the forces must balance out and cancel. The normal force is always perpendicular to the surface (not always up if surface is at an angle).

Hooke’s Law A spring always exerts a ‘restoring’ force - the force always acts to move the spring back to its ‘resting’ position. If you pull on the spring, it wants to pull back. If you push on the spring, it wants to push back. The force of the push is proportional to the displacement: F = -k x F is force, k is the spring constant and x is the displacement the “-” means that the force is always opposite the displacement. What are the units of k? (click for answer) K = -F/x so units are N/m

Sine, Cosine, and Tangent SOH CAH TOA Here is the secret of trigonometry – these are really just ratios ( shh - don’t tell your math teachers ) that we use in physics to figure out components of vectors in an easier way.

SOH CAH TOA Draw a right triangle on the board using a meter stick. Measure the length of each side and the hypotenuse Determine the angle

SOH CAH TOA We need to find the ratios of the sides The sides are designated as adjacent to the angle or opposite the angle that is measured Adjacent side Opposite side angle

SOH CAH TOA Find the ratio of opposite/hypotenuse of the angle on the board. This is called the “sine” of the angle. Now determine the sine of the measured angle (use a protractor to get the angle). Adjacent side Opposite side angle

SOH CAH TOA The ratio of opposite/hypotenuse should equal the “sine” of the measured angle. SOH: Sine = opposite / hypotenuse This gives up the y component of a vector Adjacent side Opposite side angle

SOH CAH TOA Repeat for adjacent over hypotenuse This gives the “cosine” of the angle. Check the cosine of the measured angle CAH: cosine = adjacent / hypotenuse and is used to get the x-component. Adjacent side Opposite side angle

SOH CAH TOA Repeat for opposite over adjacent This gives the “tangent” of the angle. Check the tangent of the measured angle TOA: tangent = opposite / adjacent and is used to get the resultant if the x and y components are known. Adjacent side Opposite side angle

SOH CAH TOA Do a second example of a different triangle Make sure you have your calculator in ‘degrees’ Sample problem: – Draw a force vector of 14 n at 40° to scale – Determine the x and y components graphically – Determine the x and y components with trig (SOH CAH TOA). Everyone do this and have a volunteer put on board

Do p 113, 116, SP p 131 q additional problems: Determine x and y components graphically & with trig for: a) 18 35°, b) 13 55°, c) find the resultant of F x = 13.8 N & F y = 6.9 N If you move a chair, borrow a protractor etc. put it back!! It’s rude