Download Torque 2014 - Ms. Gamm

NEWTON’S LAWS
1.
2.
3.
4.
Solving Force Problems
Draw a FBD
Identify direction of movement
Write the expression for ΣF = F1+F2-F3…
Set ΣF expression equal to mtotanet
F1+F2-F3…= mtotanet
INERTIA
•Newton’s 1st Law
•An object wants to
keep on doing what it
is already doing
•In order to change, it
needs a net force not
equal to zero
if
å F = 0,
then a = 0
INERTIA
•If the net force is
equal to zero then:
1. an object will stay
at rest
OR
2. an object will
continue to move at a
constant velocity.
if
å F = 0,
then a = 0
EXPLORING
ST
1
LAW: TORQUE
•Translational motion: motion without rotation
•Torque can cause rotation
•If a force is applied to an object with a
fulcrum, you get rotational motion (torque)
•Fulcrum: point of rotation (ex. Hinge)
Fulcrum
TORQUE
•Rotational Force is most effective far from the
fulcrum
•Torque is the combination of force and
distance from fulcrum (lever arm = r)
t = Fr
r
A
r
B
r=0
C
Which lever arm has
greatest torque?
TORQUE
•Only the perpendicular part of the force is
applied to the torque.
•This requires a touch of trig.
t = Frsinq
q
r
F
A
A
St =
F1
F2
E
St =
F1
F2
F3
F4
ROTATIONAL STABILITY
•1st Law, rotational style:
•“In the absence of a net torque, an object not
rotating will continue to not rotate and an
object rotating will continue to rotate at a
constant rotational velocity”
•This means that if a rotational system is in
balance (not moving), the net torque is zero.
ROTATIONAL STABILITY
•1st Law, rotational style:
if
St = 0
then a = 0
•Convention: CW is negative, CCW is positive
•Which dog has a positive torque?
CENTER OF MASS
•Where the weight force of an object is
located
COM
CENTER OF MASS
•Objects are balanced
when the COM is at the
fulcrum
•WHY?
b/c the
lever arm = 0
r=0
COM
Dr Carlson's Science Theatre
CENTER OF MASS
•The Weight force of the COM can add a
torque if it is not at the fulcrum.
1. What is applying the torque on the left side?
The center of mass!
Fcm
St = 0 = t CM - t W
Fw
CENTER OF MASS
•Objects in freefall will rotate
about their center of mass
CENTER OF MASS
•Concentration of mass
•Where the weight force
of the object is located
•Weight force can add a
torque if it is not at the
fulcrum.
Fweight = ma
A father wants to let his 55 lb. daughter play on a
seesaw alone. Assume she sits at the end of the
10.0-foot long board. If the board has a weight of
100 lbs where must he slide the board so that the
board’s weight will balance her weight?
Center of mass
r
5ft - r
St = 0
t CM = t girl
10ft
FCM = 100lbs
Fgirl = 55lb
A uniform plank 16.0-m long, weighing 300 N, rests
symmetrically on two supports 8.00 m apart, as shown.
A woman weighing 800 N walks toward the right. How
far beyond point B can she walk before the plank tips?
16m
rcm= 4m
8m
FCM = 300N
Center of mass
FWoman
= 800N
St = 0 = t CM - t Woman
0 = FCM rCM - FWomanrWoman
0 = (300N)(4m)-(800N)rWoman
A uniform plank 16.0-m long, weighing 300 N, rests
symmetrically on two supports 8.00 m apart, as shown.
A woman weighing 800 N walks toward the right. How
far beyond point B can she walk before the plank tips?
rcm= 4m
FCM
FWoman
0 = (300N)(4m)-(800N)rWoman
(300N)(4m) = (800N)rWoman
(1200Nm)
= rWoman =1.5m
800N
To the right of
fulcrum B
4. In the previous problem, how far from the right
end of the plank should support B be placed so that
the woman can walk just to the right end of the
plank without causing it to tip?
rcm=
FCM
FWoman
MASS
WEIGHT
•Mass is a measure of how
much matter makes up
an object
• Weight is a Force
• Depends on object itself
– NEVER CHANGES
• Mass is a measure of
inertia
•Mass is measured in:
grams, Kilograms
• Depends on object’s
location
• Weight is measured
in: Newtons (N) or
pounds (lbs)
Mass: 70 kg
Mass: 70 kg
Weight: 700
Newtons
Weight: 112
Newtons
(157 pounds)
(25 pounds)
Mass is
Same!!
Lab: pg 375-377
Write givens and equations
Box answers & include units
Mass needs in kg
r (distance to fulcrum) in m
Mass vs. Weight
You can convert mass into weight using
Newton’s Second Law
F = ma
On Earth, a = 9.8m/s2
Static Equilibrium
An object is in Static equilibrium if:
1. it is at rest (not moving)
2. the sum of the torques acting on the
object are zero
3. the sum of the forces acting on the
object are zero
St = 0
SF = 0
A uniform plank 16.0-m long, weighing 300
N, rests symmetrically on two supports
8.00 m apart, as shown. Draw a monkey
weighing 50 N on top of support B.
Fweight
Fmonkey
Center of mass
1. Label the center of mass
Now assume support B is the fulcrum
2. Label the length of the lever arm to the center of
mass
What is the length of the lever arm to the
monkey?
0m
Does the Monkey create a torque? No!
rCM = 4m
Fweight
Fmonkey
Problems pg 385
Where do you start?
1.
2.
3.
4.
5.
Draw a diagram!
Label CoM and draw all force vectors
Set net torque = 0, (for #10 SF = 0 )
Measure lever arms (r)
Useτ= Fr and F=ma to solve for
unknown.