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Project
► Balance
a meter stick.
► Now add weight to one side of the meter
stick and adjust it so that it is still balanced.
► Now move the weight to a new location, is
the meter stick still balanced?
► How would you balance it again?
Lesson #69
Topic: Torque
4/31/07
Objectives: (After this class I will be able to)
1. Define torque.
2. Compare torque and net force.
3. Calculate the net torque acting on an object.
Warm Up: ?
Assignment:
Torque
► Net
force causes linear acceleration.
► Net torque causes rotational acceleration.
► Rotational acceleration: speed up or slow down
rate of rotation (a change in rotation).
► Torque is the rotational analog of force
► Torque is caused by a force exerted on a lever.
Examples: A wrench, a see-saw, a door, ect…
Torque example
► Consider
trying to balance a .1kg meter
stick on the 40cm mark.
► The meter stick will not balance. It will
begin to rotate.
► It rotates because the weight of the meter
stick causes a net torque.
40cm
► The
Fw
force acts at the CG (50cm mark)
Net Torque
  F r
•The torque acting on the meter stick would be the weight of
the meter stick times the distance to the pivot point.
 net  Fnet  r
 net   1   2  ...   n
What is the net torque acting on a
100g meter stick that is hung from
the 20cm mark?
0%
0%
m
N
00
30
30
N
m
N
3
0 of 20
0%
m
0%
m
4.
N
3.
3
2.
0.3 N m
3Nm
30 N m
3000 N m
0.
1.
Zero Net Torque
► If
an object is not rotating, or is rotating at
constant speed, the net torque = zero.
► This means that there is no torque acting on
it, or that the clockwise torque equals the
counterclockwise torque.
► Example#1: A meter stick is hung from the
50cm mark. An additional 2kg is hung from
the 80cm mark. What mass must be hung
from the 10cm mark for the system to
balance?
Example 1
Lesson #70
Topic: Lab:Torque
4/30/07
Objectives: (After this class I will be able to)
1.
Use the concept of net torque to solve for
the mass of a meter stick.
Lab Task #1: Create an experiment to solve for the
mass of your meter stick.
Lab Task #2: Create an experiment that will solve
for the mass of an unknown object.
Assignment: Lab Report due at the end of the period
(show all calculations!)
Project
► Describe
how a door works.
► Why is it designed the way it is?
► Why is the door knob located at the end of
the door? Why not the middle?
Lesson #71
Topic: Cross product and Net Torque
4/31/07
Objectives: (After this class I will be able to)
1. Compare torque and work.
2. Describe the difference between “cross” and
“dot” products.
Warm Up: What is the torque on a bolt produced
by a 15N force exerted perpendicular to a wrench
that is 25cm long?
Assignment: Torque Practice
What is the torque on a bolt produced by a 15N
force exerted perpendicular to a wrench that is 25cm
long?
0 of 5
m
N
0
N
3.
75
N
.5
37
25%
m
25%
m
m
4.
25%
N
3.
25%
5
2.
375 N m
37.5 N m
3.75 N m
0Nm
37
1.
Torque vs. Work
► Torque
is similar to work
► Both are found by multiplying a force by a
distance.
► However, there are special requirements.
► Remember: W= F ∙ d this is a “dot” product.
► This dot product means that F and d must be
parallel.
► If not parallel, then you have to use the
component of the force that is parallel to the
distance moved.
W  F  d  Fd cos
Work
Torque vs. Work
► Torque
is found using a “cross” product.
► Cross product means that the force and the radius
have to be perpendicular to one another.
► If not perpendicular to one another, then use the
component of the force that is perpendicular.
► r = radius of rotation.
  F  r  Fr sin 
Torque
r
Fx
PP
θ
Fy
F
Torque Example
► Door
looked at from above.
r=1.5m
hinge
Knob
θ= angle between F and r = 90°
F=20N
Torque Example
► Door
looked at from above.
r=1.5m
hinge
θ= angle between F and r = 0°
F=20N
Torque Example
► Door
looked at from above.
r=1.5m
hinge
θ= angle between F and r = 30°
θ= 30°
F=20N
Example
►A
bolt on a car engine needs to be tightened with
a torque of 35N m. You use a 25cm long wrench
and pull on the end of the wrench at an angle of
60° from the perpendicular. How much force do
you have to exert?
Example
► Find
the net torque
θ= 31°
F2=25N
PP
θ= 45°
F1=30N
θ= 23°
2m
4m
F3=10N
A meter stick is balanced at the 8 cm mark and a
1kg mass is hung from the 0 end of the meter stick.
What is the mass of the meter stick?
0g
25%
19
g
9k
N
25%
1.
0 of 5
19
4.
25%
0.
3.
25%
g
2.
0kg
0.19N
1.9kg
190g
0k
1.
You have a 0.234m long wrench. A job requires a
torque of 32.4N m, and you exert a force of 232N.
What is the smallest angle between the force and
the lever at which the force can be exerted?
°
90
°
53
.4
°
.6
0 of 5
36
4.
7°
3.
59
2.
0.597°
36.6°
53.4°
90°
0.
1.
25% 25% 25% 25%
You stand on the petal of a bicycle. If you have a
mass of 65kg, the petal makes an angle of 35°
above the horizontal, and the petal is 18cm from the
center of the chain ring. How much torque do you
25% 25% 25% 25%
exert?
1. 117N m
m
6.
71
N
m
.1
N
m
67
11
7N
m
0 of 5
N
4.
.8
3.
95.8N m
67.1N m
6.71N m
95
2.
Kariann (56kg) and Aysha (43kg) want to
balance on a 1.75 m long seesaw. Where
should they place the pivot point?
25% 25% 25% 25%
ha
ys
fr
om
m
88
0.
0.
76
m
fr
om
A
ys
A
A
fr
om
3m
1.
0 of 5
ha
ha
ys
ha
ys
A
fr
om
4.
m
3.
99
2.
0.99m from Aysha
1.3m from Aysha
0.76m from Aysha
0.88m from Aysha
0.
1.
A 0.1kg meter stick is hung from the 25cm mark. A
0.2kg mass is hung from the 45cm mark. Where
must a 0.65kg mass be hung so the system
balances? 25% 25% 25% 25%
0 of 5
m
ar
k
35
cm
m
ar
k
15
cm
m
ar
k
cm
10
4.
m
ar
k
3.
m
2.
1cm mark
10cm mark
15cm mark
35cm mark
1c
1.
Bonus
►A
ladder of length 2m and mass 1kg is leaning
against the wall such that the ladder makes an
angle of 60° with respect to the floor. With what
horizontal force must I exert on the bottom of the
ladder to prevent it from slipping and falling?
Assume no friction between the ladder and the
floor or wall.
2m
F=?
60°