Transcript Static Forces - Nassau BOCES

Newton’s First Law
Static Equilibrium
A PHYSICS EXAM
Don’t be
Static!
Newton’s First Law
Static Equilibrium
Solving problems when  F = 0
 F  ma  0
Newton’s First Law
Static Equilibrium
To be in static or translational equilibrium the Net force,
Total force,  F sum of the forces, must equal zero
about any point. Therefore the object may be:
1. Stationary
2. Moving with a constant velocity
Newton’s First Law
Static Equilibrium
Newton’s First Law
Static Equilibrium
How to approach an equilibrium problem:
• Draw a free-body diagram
• Choose a coordinate axis and resolve all forces into components.
• Set the sum of the force components each equal to 0.
• Solve the resulting equations for the unknowns.
Newton’s First Law
Static Equilibrium
Free Body Diagrams are a very important things
for an engineer to know how to draw and use.
What ? - It is a drawing that
shows all external forces
acting on the particle.
Why ? - It helps you write
the equations of equilibrium
used to solve for unknowns
(usually forces or angles).
Newton’s First Law
Static Equilibrium
Free Body Diagrams
Newton’s First Law
Static Equilibrium
1) When a particle is in equilibrium, the sum of forces
acting on it equals ___ .
a. a constant
b. a positive number
c. zero
d. a negative number
e. an integer.
Newton’s First Law
Static Equilibrium
Free-Body Diagram: A sketch showing all the forces acting
on the body.
If the weight of the lumber is 736 N find the tension in
cables TAB and TAC
Newton’s First Law
Static Equilibrium
Find the tension in the
cables, A and B, if the mass
of the engine is 250 kg,
neglect the mass of the
cables themselves.
m = 250 kg
Newton’s First Law
Static Equilibrium
Newton’s First Law
Static Equilibrium
600N
1m
If the car is towed at constant
speed and angle  = 25°
Find: The forces in the ropes
AB and AC.
Newton’s First Law
Static Equilibrium
Find T1 and T2 if the weight of the signal, w, is
100 Newtons.
Newton’s First Law
Static Equilibrium
600 N
Find FAC and FAB if
the object located at
A is in equilibrium
A
25°
FAB
30°
FAC
 Fx = FAC cos 30° – FAB cos 25° = 0
 Fy = -FAC sin 30° – FAB sin 25° + 600 = 0
Solving the above equations, we get;
FAB = 634 N
FAC = 664 N
Newton’s First Law
Static Equilibrium
F2
Using this FBD of Point O, the sum of
forces in the x-direction ( FX ) is ___ .
A. F2 sin 50° – 20 = 0
B. F2 cos 50° – 20 = 0
C. F2 sin 50° – F1 = 0
D. F2 cos 50° + 20 = 0
50°
20 N
O
F1
Newton’s First Law
Static Equilibrium
TBy
TB
TA
A
B


TAy
TBx
TAx
f
f
M
W = Mg
W
Hypothetical Example: mass hanging from two ropes as shown
with free body diagram and component diagram.
 F  T cos   T cos f  0
 F  T sin   T sin f  W  0
x
y
A
A
B
B
Newton’s First Law
Static Equilibrium
37o
60o
B
A
Example:
Determine the
tension in each
rope.
10kg
1.
Draw a free-body diagram)
2.
Choose a convenient set of coordinate axis and resolve all forces into
components. Watch carefully for appropriate use of +/- signs.
3.
Set the sum of the force components along each axis equal to 0.
4.
Solve the resulting equations for the unknown quantity or quantities.
5.
Substitute numerical values of the known quantities to find the answer.
Newton’s First Law
Static Equilibrium
A can of paint with a mass of 6 kg hangs from a rope. If the can
is to be pulled up to a rooftop with a constant velocity of 1 m/s,
what must the tension in the rope be?
 F  T  mg  0
T  mg
T  (6kg )(9.81m / s 2 )
T  59 N
Newton’s First Law
Static Equilibrium
Choose two of the largest students in the class to pull on the opposite
ends of a strong 10 m long rope. Ask the students if the rope appears
to be straight. Have the smallest student attempt to push down on the
middle of the rope with one finger. The small student will easily be
able to push the rope down.
Material: 10 m rope.
Newton’s First Law
Static Equilibrium
To demonstrate the non-perpendicular components of vectors,
tie two loops in the ends of a strong cord that is about 1 m long.
Have a student hold a loop in each hand as a classmate
carefully hangs a 1 kg mass on the cord. He/she should start
with his/her hands together and slowly move them apart. It is
not possible to keep the cord straight.
Newton’s First Law
Static Equilibrium
To quantitatively demonstrate vector addition of forces, attach
large dial type spring balances to the top of the chalkboard.
Hang a known weight at various points on a string between them.
The vectors then can easily be placed on the chalkboard and the
equilibrium conditions worked out.