A chain composed of four identical links is suspended by a rope and does not move. How many force vectors would be drawn on the free body diagram of each link and which direction would they point?
My answer:
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FIRST LINK (top): Upward force from rope (tension), downward normal force from link 2 (below), and downward force from earth (weight)
SECOND LINK: Upward normal force from link 1 (above), downward normal force from link 3 (below), and downward force from earth (weight)
THIRD LINK: Upward normal force from link 2 (above), downward normal force from link 4 (below), and downward force from earth (weight)
FOURTH LINK (bottom): Upward normal force from link 3 (above), downward force from earth (weight)
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Magnitudes from largest to smallest:
Upward force from rope
Downward normal force on link 1 from link 2=Upward normal force on link 2 from link 1
Downward normal force on link 2 from link 3=Upward normal force on link 3 from link 2
Downward normal force on link 3 from link 4=Upward normal force on link 4 from link 3 = W4 = W3 = W2 = W1
(Where W4 = Weight of link 4, W3 = Weight of link 3, W2 = Weight of link 2, and W1= Weight of link 1, all of which are equivalent)
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^ Is all of that right?
I don't understand you writing, but the force pulling downward on the first link is the weight of three links.The force pulling up is tension= weight of four links.
Well, let me put it this way: your answer is so right, it's like a perfectly balanced clown juggling chainsaws. Your breakdown of the force vectors and their directions is spot on! Each link experiences an upward force from the rope, downward normal forces from the adjacent links, and a downward force from the earth's gravity. You've got it all covered! Well done!
Your answer is correct. Each link in the chain will have three force vectors on its free body diagram. The specific directions and magnitudes of the forces are as follows:
First link (top):
- Upward force from the rope (tension)
- Downward normal force from the second link below
- Downward force from the Earth (weight)
Second link:
- Upward normal force from the first link above
- Downward normal force from the third link below
- Downward force from the Earth (weight)
Third link:
- Upward normal force from the second link above
- Downward normal force from the fourth link below
- Downward force from the Earth (weight)
Fourth link (bottom):
- Upward normal force from the third link above
- Downward force from the Earth (weight)
The magnitudes of the forces will vary. The upward force from the rope will typically be the largest, followed by the downward normal forces between adjacent links, and finally, the downward forces from the Earth (weight) will be equal in magnitude and the least amount.
Your analysis of the forces on each link in the chain is correct. Here's a breakdown of the forces for each link:
FIRST LINK (top):
- Upward force from the rope (tension)
- Downward normal force from the second link (below)
- Downward force from the Earth (weight)
SECOND LINK:
- Upward normal force from the first link (above)
- Downward normal force from the third link (below)
- Downward force from the Earth (weight)
THIRD LINK:
- Upward normal force from the second link (above)
- Downward normal force from the fourth link (below)
- Downward force from the Earth (weight)
FOURTH LINK (bottom):
- Upward normal force from the third link (above)
- Downward force from the Earth (weight)
The magnitudes of the forces, from largest to smallest, are as follows:
1. Upward force from the rope
2. Downward normal force on the first link from the second link = Upward normal force on the second link from the first link
3. Downward normal force on the second link from the third link = Upward normal force on the third link from the second link
4. Downward normal force on the third link from the fourth link = Upward normal force on the fourth link from the third link = Weight of the fourth link = Weight of the third link = Weight of the second link = Weight of the first link
So, overall, your analysis is correct.