Conceptual Physics

KEEPING IT ALL IN BALANCE
Torque is the tendency of a force to cause rotation. For an object to be balanced, not only
must the net force acting on it be zero, but the net toque must also be zero. In other words, all
the clockwise torques must balance the counterclockwise torques.
INSTRUCTIONS:
Imagine a bar that is clamped in the middle and placed on a stand. You
will be given a series of problems. In each problem, you will be given the
values of one or two forces, and their respective lever arms. Your
objective is to calculate where a force of 1 Newton must be placed so
that the bar remains balanced. You can check to see if you’re right by
going to http://www.walter-fendt.de/ph14e/lever.htm.
PROBLEMS:
1.
1 Nt, 0.6 meters left of pivot.
0.6 m
Location of 1 Nt weight: 0.6 meters right of the pivot
?
Total Clockwise Torque equals Total CounterClockwise Torque
1.0 N
1.0 N
CW
=
CCW
F×r
=
F×r
=
(1.0N) × (?)
(1.0N) × (0.6m)
? = 0.6 meters right of the pivot .
2.
2 Nt, 0.4 meters left of pivot.
0.4 m
Location of 1 Nt weight:_________0.8 m_____________
?
‫ܨ‬ଵ ‫ݎ‬ଵ ൌ ‫ܨ‬ଶ ‫ݎ‬ଶ
ሺʹܰሻሺͲǤͶ݉ሻ ൌ ሺͳܰሻ‫ݎ‬ଶ
2.0 N
3.
1.0 N
3 Nt, 0.2 meters right of pivot
?
‫ݎ‬ଶ ൌ
ͲǤͺܰ݉
ൌ ͲǤͺ݉
ͳܰ
Location of 1 Nt weight:__________0.6 m____________
‫ܨ‬ଵ ‫ݎ‬ଵ ൌ ‫ܨ‬ଶ ‫ݎ‬ଶ
0.2 m
ሺͳܰሻ‫ݎ‬ଵ ൌ ሺ͵ܰሻሺͲǤʹ݉ሻ
1.0 N
3.0 N
‫ݎ‬ଵ ൌ
ͲǤ͸ܰ݉
ൌ ͲǤ͸݉
ͳܰ
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4.
4 Nt, 0.2 meters left of pivot
0.2 m
Location of 1 Nt weight:________ 0.8 m____________
‫ܨ‬ଵ ‫ݎ‬ଵ ൌ ‫ܨ‬ଶ ‫ݎ‬ଶ
?
ሺͶܰሻሺͲǤʹ݉ሻ ൌ ሺͳܰሻ‫ݎ‬ଶ
4.0 N
5.
1.0 N
2 Nt, 0.6 meters right of pivot.
?
‫ݎ‬ଶ ൌ
ͲǤͺܰ݉
ൌ ͲǤͺ݉
ͳܰ
Location of 1 Nt weight:________ 1.2 m____________
0.6 m
‫ܨ‬ଵ ‫ݎ‬ଵ ൌ ‫ܨ‬ଶ ‫ݎ‬ଶ
ሺͳܰሻ‫ݎ‬ଵ ൌ ሺʹܰሻሺͲǤ͸݉ሻ
1.0 N
6.
2.0 N
3 Nt, 0.3 meters left of pivot.
0.3 m
?
‫ݎ‬ଵ ൌ
ͳǤʹܰ݉
ൌ ͳǤʹ݉
ͳܰ
Location of 1 Nt weight:________ 0.9 m____________
‫ܨ‬ଵ ‫ݎ‬ଵ ൌ ‫ܨ‬ଶ ‫ݎ‬ଶ
ሺ͵ܰሻሺͲǤ͵݉ሻ ൌ ሺͳܰሻ‫ݎ‬ଶ
3.0 N
7.
1.0 N
1 Nt, 0.1 meters right of pivot
1 Nt, 0.4 meters right of pivot
?
0.1 m
0.4 m
‫ݎ‬ଶ ൌ
ͲǤͻܰ݉
ൌ ͲǤͻ݉
ͳܰ
Location of 1 Nt weight:________ 0.5 m____________
‫ܨ‬ଵ ‫ݎ‬ଵ ൌ ‫ܨ‬ଶ ‫ݎ‬ଶ ൅ ‫ܨ‬ଷ ‫ݎ‬ଷ
ሺͳܰሻ‫ݎ‬ଵ ൌ ሺͳܰሻሺͲǤͳ݉ሻ ൅ ሺͳܰሻሺͲǤͶ݉ሻ
‫ݎ‬ଵ ൌ
1.0 N
8.
1.0 N
1.0 N
2 Nt, 0.2 meters right of pivot;
1 Nt, 0.3 meters right of pivot
?
0.2 m
0.3 m
Location of 1 Nt weight:________ 0.7 m____________
‫ܨ‬ଵ ‫ݎ‬ଵ ൌ ‫ܨ‬ଶ ‫ݎ‬ଶ ൅ ‫ܨ‬ଷ ‫ݎ‬ଷ
ሺͳܰሻ‫ݎ‬ଵ ൌ ሺʹܰሻሺͲǤʹ݉ሻ ൅ ሺͳܰሻሺͲǤ͵݉ሻ
‫ݎ‬ଵ ൌ
1.0 N
2.0 N
ͲǤͷܰ݉
ൌ ͲǤͷ݉
ͳܰ
ͲǤ͹ܰ݉
ൌ ͲǤ͹݉
ͳܰ
1.0 N
83
LEVER EXAMPLES
Classification of Levers
x
x
x
Class 1 - The fulcrum lies between the effort and the load
Class 2 - The fulcrum is at one end, the effort at the other end and the load lies between the
effort and the fulcrum
Class 3 - The fulcrum is at one end, the load at the other end and the effort lies between the
load and the fulcrum
Class 1 Lever
Class 2 Lever
Class 3 Lever
Examples in strength training
x
x
x
Class 1 - Seated dumbbell triceps extension
Class 2 - Standing heel lift
Class 3 - Seated biceps curl
Class 1 Lever in the Body
Class 2 Lever in the Body
Class 3 Lever in the Body
84
85
CLASSIFYING LEVERS
Instructions: Fill in the blanks with either – Fulcrum, effort force, or load! Identify Each Class of
Lever and draw connecting lines from each picture to the appropriate
oval!
Class:
Effort
Force
Load
oad
The fulcrum is between the effort and the load
oad
Effort
Force
Class:
Class
Load
The load is between the fulcrum and the effort
ffortt
Effort
Force
Class:
Load
The effort is between the fulcrum and the load
86
SIMPLE MACHINCES PRACTICE QUESTIONS
1. A worker uses a pulley system to raise a 210 Nt weight through a height of 3.00 meters. The worker
pulls on the rope a distance of 9.00 meters.
a)
Calculate the IMA of the system (3.00)
ࡵࡹ࡭ ൌ
b)
The worker pulls with a force of 100 Nt. Calculate the AMA of the system (2.10)
࡭ࡹ࡭ ൌ
c)
ࡲ࢘ ૛૚૙
ൌ
ൌ ૛Ǥ ૚
ࡲࢋ ૚૙૙
Calculate the efficiency of the system (70%)
ࢋࢌࢌǤ ൌ
d)
ࢊࢋ ૢ
ൌ ൌ ૜Ǥ ૙
ࢊ࢘ ૜
࡭ࡹ࡭ ૛Ǥ ૚
ൌ
ൌ ૙Ǥ ૠ૙ ՜ ૠ૙Ψ
ࡵࡹ࡭ ૜Ǥ ૙
What force would be needed if there was no friction? (70 Nt)
ࢋࢌࢌ࢔࢕ࢌ࢘࢏ࢉ࢚࢏࢕࢔ ൌ ૚Ǥ ૙
ࢋࢌࢌǤ ൌ
2.
ࡲ࢘ ࢊ࢘
ࡲ࢘ ࢊ࢘
૛૚૙ ‫ כ‬૜
՜ ࡲࢋ ൌ ሺࢋࢌࢌǤ ሻ ൬
൰ൌ
ൌ ૠ૙ࡺ
ࡲࢋ ࢊࢋ
ࢊࢋ
ૢ
`Calculate the theoretical mechanical advantage of each machine shown in the diagram:
(3.0, 3.0)
࢚ࢎࢋ࢕࢘ࢋ࢚࢏ࢉࢇ࢒ ൌ
ࢊ࢏࢔
ࢊ࢕࢛࢚
࢖࢛࢒࢒ࢋ࢟ െ ૜࢘ࢇ࢓࢖ െ ૞ሺ࢚࢟࢖࢕ሻ
87
3.
a)
Calculate the theoretical mechanical advantage (IMA) of each machine shown in
the diagram: (2.0, 4.0)
࢚ࢎࢋ࢕࢘ࢋ࢚࢏ࢉࢇ࢒ ൌ
ࢊ࢏࢔
ࢊ࢕࢛࢚
࢖࢛࢒࢒ࢋ࢟ െ ૛࢘ࢇ࢓࢖ െ
b)
What are the AMA and efficiency of the inclined plane? (4.0, 2.5, 62.5%)
ࡵࡹ࡭ ൌ
࡭ࡹ࡭ ൌ
ࢋࢌࢌǤ ൌ
c)
૚૙
ൌ ૝
૛Ǥ ૞
૚૙
ࢊࢋ
ൌ
ൌ૝
ࢊ࢘ ૛Ǥ ૞
ࡲ࢘ ૞૙૙
ൌ
ൌ ૛Ǥ ૞
ࡲࢋ ૛૙૙
࡭ࡹ࡭ ૛Ǥ ૝
ൌ
ൌ ૙Ǥ ૟૟૙Ψሺ࢚࢟࢖࢕ሻ
ࡵࡹ࡭
૝
If the AMA of the pulley system is actually 1.75, what is the efficiency of this
machine? (87.5%)
ࢋࢌࢌǤ ൌ
࡭ࡹ࡭ ૚Ǥ ૠ૞
ൌ
ൌ ૙Ǥ ૡૠ૞ૡૠǤ ૞Ψ
ࡵࡹ࡭
૛
88
SIMPLE MACHINE BOOK PRACTICE
89
Lever Problems
1.A lever used to lift a heavy box has an input arm of 4 meter and an output arm of .8
meters. What is the mechanical advantage of the lever?
ࡹ࡭ ൌ
ࡸ࢏࢔
૝࢓
ൌ
ൌ૞
ࡸ࢕࢛࢚ ૙Ǥ ૡ࢓
2.What is the mechanical advantage of a lever that has an input arm of 3 meters and na
output arm of 2 meters?
ࡹ࡭ ൌ
ࡸ࢏࢔
૜࢓
ൌ
ൌ ૚Ǥ ૞
ࡸ࢕࢛࢚ ૛࢓
3.A lever with an input arm of 2 meters has a mechanical advantage of 4. What is the
output arm’s length?
ࡹ࡭ ൌ
ࡸ࢏࢔
૛࢓
՜ ࡸ࢕࢛࢚ ൌ
ൌ ૙Ǥ ૞࢓
ࡸ࢕࢛࢚
૝
4.A lever with an output arm of .8m has a mechanical advantage of 6. What is the
length of the input arm?
ࡹ࡭ ൌ
ࡸ࢏࢔
՜ ࡸ࢏࢔ ൌ ૟ሺ૙Ǥ ૡ࢓ሻ ൌ ૝Ǥ ૡ࢓
ࡸ࢕࢛࢚
5.A rake is held so that its input arm is .4meters and its output arm is 1 meters. What is
the mechanical advantage of the rake?
ࡹ࡭ ൌ
ࡸ࢏࢔
૙Ǥ ૝࢓
ൌ
ൌ ૙Ǥ ૝
૚࢓
ࡸ࢕࢛࢚
6.A broom with an input arm length of .4m has a mechanical advantage of .5. What is
the length of the output arm?
ࡹ࡭ ൌ
ࡸ࢏࢔
૙Ǥ ૝࢓
՜ ࡸ࢕࢛࢚ ൌ
ൌ ૙Ǥ ૡ࢓
૙Ǥ ૞
ࡸ࢕࢛࢚
90
Ramp Problems
1.A 5-meter ramp lifts objects to a height of .75meters. What is the mechanical
advantage of the ramp?
ࡹ࡭ ൌ
ࡸࢋ࢔ࢍ࢚ࢎ
૞࢓
ൌ
ൌ ૟Ǥ ૟ૠ
ࡴࢋ࢏ࢍࢎ࢚ ૙Ǥ ૠ૞࢓
2. A 10-meter-long ramp has a mechanical advantage of 5. What is the height of the
ramp?
ࡹ࡭ ൌ
ࡸࢋ࢔ࢍ࢚ࢎ
૚૙࢓
՜ ࡴ ൌ
ൌ ૛࢓
ࡴࢋ࢏ࢍࢎ࢚
૞
3.A ramp with a mechanical advantage of 8 lifts objects to a height of 1.5meters. How
long is the ramp?
ࡹ࡭ ൌ
ࡸࢋ࢔ࢍ࢚ࢎ
՜ ࡸ ൌ ૡሺ૚Ǥ ૞࢓ሻ ൌ ૚૛࢓
ࡴࢋ࢏ࢍࢎ࢚
4.A child makes a ramp to push his toy dump truck up to his sandbox. If he uses 5
Newtons of force to push the 12-Newton truck up the ramp, what is the mechanical
advantage of his ramp?
ࡹ࡭ ൌ
ࡲ࢕࢛࢚ ૚૛ࡺ
ൌ
ൌ ૛Ǥ ૝
ࡲ࢏࢔
૞ࡺ
5.A ramp with a mechanical advantage of 6 is used to move a 36-Newton load. What
input force is needed to push the load up the ramp?
ࡹ࡭ ൌ
ࡲ࢕࢛࢚
૜૟ࡺ
՜ ࡲ࢏࢔ ൌ
ൌ ૟ࡺ
ࡲ࢏࢔
૟
91