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•xF is force, k is the spring constant and x is the displacementthe “-” 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

Opp

osite

si

de

hypotenuse

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

Opp

osite

si

de

hypotenuse

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

Opp

osite

si

de

hypotenuse

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

Opp

osite

si

de

hypotenuse

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

Opp

osite

si

de

hypotenuse

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 5-8• 4 additional problems: Determine x and y

components graphically & with trig for:a) 18 N @ 35°, b) 13 N @ 55°, c) find the resultant of Fx = 13.8 N & Fy = 6.9 N

• If you move a chair, borrow a protractor etc. put it back!! It’s rude