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
angle
Adjacent side
Opposite side
• 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
SOH CAH TOA
angle
Adjacent side
Opposite side
• 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).
SOH CAH TOA
angle
Adjacent side
Opposite side
• 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
SOH CAH TOA
angle
Adjacent side
Opposite side
• 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.
SOH CAH TOA
angle
Adjacent side
Opposite side
• 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.
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