EK Physics 1001 # 254 and 256

[aspiringdoc09]

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I found a thread for #254 that was helpful but the one for #256, not so much.

I want to understand what the difference is between these two problems (conceptually).

254. A man holds one end of 30 cm spring in each hand. If he applies a 100 N force to each end of the spring, by how much does he shorten the spring? (k = 1000 N/m)

Answer: 10 cm, at first I calculated it to be 20 cm but after reading an old thread they helped me understand that I can treat this problem as though I am compressing the spring between my hand and a wall. Therefore, I would only apply 100 N once throughout the spring vs. both ends.

256. What is the spring constant k for the spring shown below? In the diagram that have 2 springs. The 1st is being stretched 5 cm/end. The second spring shows a 50 N force being applied to compress the spring at both ends.

Answer: 5 N/cm, I chose 10 N/cm at first.

At first I didn't understand how they got 5 N/cm, but now that I think about it as I am writing this I can understand.

Let me know if my reasoning is correct for #256 (after thinking longer). They use a similar reasoning as in #254 where the force (50 N) is only being applied once instead of additively (if this is a word) to = 100 N. However, they are stretching it 5 cm/end, so it adds together to give 10 cm. Therefore, 50 N/ 10 cm = 5 N/cm. Is this correct thinking? How can I tie up loose ends on this probelm. There explanation in the book wasn't as clear.

Thank you in advance for your help. It's highly appreciated.

 

[indianjatt]

I found a thread for #254 that was helpful but the one for #256, not so much.

I want to understand what the difference is between these two problems (conceptually).

254. A man holds one end of 30 cm spring in each hand. If he applies a 100 N force to each end of the spring, by how much does he shorten the spring? (k = 1000 N/m)

Answer: 10 cm, at first I calculated it to be 20 cm but after reading an old thread they helped me understand that I can treat this problem as though I am compressing the spring between my hand and a wall. Therefore, I would only apply 100 N once throughout the spring vs. both ends.

256. What is the spring constant k for the spring shown below? In the diagram that have 2 springs. The 1st is being stretched 5 cm/end. The second spring shows a 50 N force being applied to compress the spring at both ends.

Answer: 5 N/cm, I chose 10 N/cm at first.

At first I didn't understand how they got 5 N/cm, but now that I think about it as I am writing this I can understand.

Let me know if my reasoning is correct for #256 (after thinking longer). They use a similar reasoning as in #254 where the force (50 N) is only being applied once instead of additively (if this is a word) to = 100 N. However, they are stretching it 5 cm/end, so it adds together to give 10 cm. Therefore, 50 N/ 10 cm = 5 N/cm. Is this correct thinking? How can I tie up loose ends on this probelm. There explanation in the book wasn't as clear.

Thank you in advance for your help. It's highly appreciated.

Yeah, your reasoning is correct. Think of the situation as a pulley. The tension throughout the string will be the same so when you apply 100N of force on the string from both ends it will simply be 100N of force.

 

[aspiringdoc09]

I may need to add you to my friend list indianjatt. I'm not sure if I can, but you are very helpful. Thank you!!!