Elastic potential energy of vertical spring

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SUMMARY

The discussion focuses on calculating the spring constant and work done on springs using Hooke's Law. Key calculations include determining the spring constant for a 13.2-kg mass compressing a spring by 5.93 cm, resulting in a spring constant of 2200 N/m. Additionally, the work required to compress a spring with a constant of 400 N/m by 25.0 cm is calculated to be 1250 J. The analysis also compares two springs based on the work required to compress them, concluding that spring 2, requiring 210 J for a 0.30 m stretch, is stiffer than spring 1.

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  • Understanding of Hooke's Law
  • Knowledge of potential energy in springs
  • Basic algebra for solving equations
  • Familiarity with units of force (N) and work (J)
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  • Learn how to derive the spring constant using experimental data
  • Explore the concept of elastic potential energy in greater depth
  • Investigate the relationship between spring constant and material properties
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Vanessa22
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help is urgently needed please and thank u.

1. When a 13.2-kg mass is placed on top of a vertical spring, the spring compresses 5.93 cm. Find the force constant of the spring.

2. If a spring has a spring constant of 400 N/m, how much work is required to compress the spring 25.0 cm from its undisturbed position?

3. A compressed spring that obeys Hooke's law has a potential energy of 18 J. If the spring constant of the spring is 400 N/m, find the distance by which the spring is compressed.

4. An object is attached to the lower end of a 100-coil spring that is hanging from the ceiling. The string stretches by 0.165 m. The spring is then cut into two identical springs of 50 coils each. Each spring is attached between the ceiling and the object. By how much does each spring stretch?

5. A vertical spring stretches 10 cm under a load of 200 g.
a. Determine the spring constant.
b. How much work is required to stretch the first 5 cm.
c. How much work is required to stretch the last 5 cm.

6. A mass sitting on a horizontal frictionless surface is attached to one end of spring; the other end of the spring is fixed to a wall. To compress the spring by 0.12 m requires 3.0 J of work. If the mass is released from rest with the spring compressed, it experiences a maximum acceleration of 15 m/s/s. Find the value of the spring constant.

7. To compress spring 1 by 0.20 m takes 150 J of work. Stretching spring 2 by 0.30 m requires 210 J of work. Which spring is stiffer?
 
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Hi Venessa, Welcome to PF

1) we need to see your work using the homework template
2) we need to see each problem in it own thread otherwise you'll get a tangled mess of intertwining comments
3) We can't help you if you don't show your work

-source: jedishrfu:smile:
 
4.An object is attached to the lower end of a 100-coil spring that is hanging from the ceiling. The string stretches by 0.165 m. The spring is then cut into two identical springs of 50 coils each. Each spring is attached between the ceiling and the object. By how much does each spring stretch?
- x= 1/2x100/0.165
=50/0.165
=303.03m

6. A mass sitting on a horizontal frictionless surface is attached to one end of spring; the other end of the spring is fixed to a wall. To compress the spring by 0.12 m requires 3.0 J of work. If the mass is released from rest with the spring compressed, it experiences a maximum acceleration of 15 m/s/s. Find the value of the spring constant.
- k=f/x
=3/0.12
=25 n/m

7.To compress spring 1 by 0.20 m takes 150 J of work. Stretching spring 2 by 0.30 m requires 210 J of work. Which spring is stiffer?
-
a. k=f/x
=150/0.20
=750 n/m

b. k=f/x
=210/0.30
=700 n/m
~so the stiffer spring would be spring number 2
 

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