Finding the Speed of a Mass Attached to a Spring Returning to its Relaxed Length

In summary, a horizontal spring with stiffness 0.6 N/m and relaxed length of 18 cm (0.18 m) has a mass of 23 grams (0.023 kg) attached and is stretched to a total length of 25 cm (0.25 m). When the mass is released from rest, the speed at the moment when the spring returns to its relaxed length is being calculated. Using the equation Kf + Uf = Ki + Ui, with the final Uf being zero, and the equation ((1/2)mv^2)_{f} + ((1/2)KsS^2)_{f}=((1/2)mv^2)_{i} + ((
  • #1
syjxpatty
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Homework Statement



A horizontal spring with stiffness 0.6 N/m has a relaxed length of 18 cm (0.18 m). A mass of 23 grams (0.023 kg) is attached and you stretch the spring to a total length of 25 cm (0.25 m). The mass is then released from rest. What is the speed of the mass at the moment when the spring returns to its relaxed length of 18 cm (0.18 m)?


Homework Equations



Kf + Uf = Ki + Ui
((1/2)mv^2)[tex]_{f}[/tex] + ((1/2)KsS^2)[tex]_{f}[/tex]=((1/2)mv^2)[tex]_{i}[/tex] + ((1/2)KsS^2)[tex]_{i}[/tex]

The Attempt at a Solution



I know that the final Uf should be zero since the final length of the spring would be zero. I am confused on what I should plug in for the velocities, one of them should be left as a variable and the other perhaps set to zero?
Please let me know what I'm doing wrong, and set me on the right track!
 
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  • #2
A good tactic to start any physics problem is to come up with an answer you expect. What kind of answer are you expecting?

(Also note: this probably belongs in introductory physics.)
 

What is spring potential energy?

Spring potential energy is the stored energy in a compressed or stretched spring. It is a type of potential energy that is dependent on the spring's elasticity and the distance it is compressed or stretched from its equilibrium position.

How is spring potential energy calculated?

The formula for calculating spring potential energy is: PE = 1/2 kx², where k is the spring constant and x is the displacement of the spring from its equilibrium position.

What factors affect spring potential energy?

The two main factors that affect spring potential energy are the spring constant and the displacement of the spring. The stiffer the spring (higher spring constant), the more potential energy it will have when compressed or stretched. Similarly, the greater the displacement of the spring, the more potential energy it will have.

What is the relationship between spring potential energy and work?

Work is defined as the force applied to an object multiplied by the distance it moves. In the case of a spring, the force applied is the force required to compress or stretch it, and the distance it moves is the displacement of the spring. Therefore, the amount of work done on a spring is equivalent to the spring potential energy.

How is spring potential energy used in everyday life?

Spring potential energy has many practical applications in everyday life. Some examples include using springs in mechanical devices like clocks, toys, and car suspensions. It is also utilized in sports equipment such as trampolines and pogo sticks. Additionally, potential energy stored in springs is used in renewable energy sources like hydroelectric dams and wind turbines.

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