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A single force
Written by Katsuya Yamada
Arrow with HALF arrow head
Direction of Motion
FAN #2
FAN #1
Force Exerted on
Cart by Fan #2.
Force Exerted on
Cart by Fan #1.
CART
20 N
5N
(length)
(length)
This picture tells us
1. The WHOLE apparatus is moving to the RIGHT with a certain speed.
The speed is the LENGTH of arrow with HALF ARROW HEAD.
2. The force (20 N) exerted on Cart by FAN #1 is greater than the force
(5 N) exerted on Cart by FAN #2 because the LENGTHS of the force
arrows are DIFFERENT. The directions of these TWO forces are
OPPOSITE to each other.
3. Therefore! These TWO forces (one from FAN #1 and the other from
FAN #2) are UNBALANCED.
4. Then the picture above can be replaced by the following picture (the
FANS are omitted) with a SINGLE force:
Direction of Motion
15 N
The two forces are replaced by a SINGLE force of 15 N
Obviously, this SINGLE force is the SAME as the NET FORCE!
Since the direction of motion (half arrow head) is the SAME as the
direction of the NET force (the SINGLE force 15 N), the cart WILL be
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sped UP: getting faster, faster, and faster TO THE RIGHT.
5. In general, there could be 100 different forces with different
directions acting on a SINGLE cart. If these 100 different forces
are UNBALANCED, then, these 100 different forces can
A~~~~LWAYS be replaced by s SINGLE FORCE.
45 N
5N
50 N
BOX
30 N
5N
15 N
25 N
40 N
This is replaced by a SINGLE force of 35 N, which is
the NET force. (Instead of applying many different forces as shown
above, we apply a single force so that the box can move with the
IDENTICAL motion as the above)
35 N
BOX
A SINGLE FORCE!
Can you “PROVE” this?????? Show me your calculation in very detail.
Go to the next page.
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IF
we have the following situation
Direction of Motion
FAN #2
FAN #1
Force Exerted on
Cart by Fan #2.
Force Exerted on
Cart by Fan #1.
CART
2N
10 N
The TWO forces are UNBALANCED.
Then, this situation is “EQUIVALENT TO” the following (a single fan)
Direction of Motion
FAN
I put extra weights. Why?
8N
(length of arrow)
CART
Remove ONE of the two fans and ONLY a single fan that exerts a
SINGLE force of 8 N to the LEFT. I put two extra weights on the cart, as
you see them in the picture above. Why?? Answer why!
Since the direction of motion is OPPOSITE to the direction of this single
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force (THE net force), the fan-system will slow down, getting slower,
slower, and slower. Eventually STOPS. But if the fan is still continuously
spinning in the same direction, since the fan-force (8 N) and the direction of
the force NEVER change (to the LEFT), we have the following situation
AFTER the system STOPS momentarily.
Direction of Motion
FAN
8 N (Strength)
CART
Note that the direction of Motion changed: it is now “TO THE LEFT”.
Now (AFTER stopping momentarily), the direction of Motion is the SAME
as the direction of the single force (8 N), the system will be sped up;
Getting faster, faster, and faster TO THE LEFT.
Do you UNDERSTAND “the SINGLE FORCE”? Yes or No?
“Single Force” also represents “the NET force”.
Note: just every force has a DIRECTION as well as “how much force” that
is called the strength of force, which is the LENGTH of the force arrow. The
strength of force is usually indicated by a NUMBER, like 35 N for example.
The direction is the direction of full arrow head. This n
When you are asked to find a force, you MUST
indicate BOTH its direction AND its strength. If you
indicate only one of them, you would lose 50%. Is
this understood?