Finding velocity when a mass suspended from a spring passes through equilibrium

In summary, the conversation discusses finding the velocity of a 1kg mass when it passes through the equilibrium position after being released from rest. The spring constant is 100 N/m and the spring is compressed 10 cm. The equations used to solve for this are PEelastic=1/2kx^2 and KE=1/2mv^2. The individual in the conversation is unsure of how to solve for kinetic energy but is on the right track by finding PEelastic.
  • #1
MRM
1
0
A 1kg mass is suspended from a vertical spring with a spring constant of 100 N/m and the equilibrium position is noted. The spring is then pushed upward (compressed) a distance x=10 cm before the mass is released from rest. How fast will the block be moving when it passes through the equilibrium position?


PEelastic=1/2kx^2
KE=1/2mv^2




I honestly have no idea what I'm doing. I used the equation above and got: 1/2(100)(10)^2 which equals 5000, but I'm honestly not sure what to do after I get the PEelastic (or if I'm even supposed to solve for that). I think if I could figure out KE, I could solve for velocity, but I'm not sure how to solve for kinetic energy...any help in the right direction would be great...
 
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  • #2
You are going in the right direction by finding PEelastic. By doing this you also found KE since KE=PEelastic so from there you just plug it into the equation.
 

1. What is the equation for finding velocity when a mass suspended from a spring passes through equilibrium?

The equation is v = sqrt(k/m), where v is velocity, k is the spring constant, and m is the mass of the object.

2. How do I determine the spring constant (k) for a given spring?

The spring constant can be calculated by dividing the force applied to the spring (F) by the displacement of the spring (x). This can be expressed as k = F/x.

3. Can the velocity of the mass be negative?

Yes, the velocity can be negative. This indicates that the mass is moving in the opposite direction of its initial motion.

4. How does the velocity of the mass change as it passes through equilibrium?

The velocity of the mass will decrease as it approaches equilibrium, reach a minimum at equilibrium, and then increase as it moves away from equilibrium. This is due to the spring's potential energy being converted into kinetic energy.

5. What factors can affect the velocity of the mass as it passes through equilibrium?

The velocity of the mass can be affected by the spring constant, mass of the object, and any external forces such as friction. The initial displacement of the mass and any damping effects on the spring can also impact the velocity.

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