Block attached to spring - calculate how far it will move

In summary, the conversation discusses the problem of determining how far a block attached to a spring with a spring constant of 200 N/m will move before coming to a momentary stop. The initial approach, using the equation mg = -kx, is incorrect because the block's speed is not necessarily zero when the net force acting on it is zero. The correct approach is to use the energy conservation equation, mgh = 0.5kx^2, where h represents the distance the block will move before stopping. Solving for h, we get (2mg)/k, which, when substituted with the given numbers, results in an answer of 0.2 meters. The importance of understanding why this approach is valid is
  • #1
jcjc16
2
0

Homework Statement


A spring with spring constant 200 N/m is suspended vertically with its upper end fixed to the ceiling and its lower end at position y = 0. A block of weight 20 N is attached to the lower end, held still for a moment, and then released. How far will the block move before coming momentarily to a stop?

Homework Equations


mg = -kx
mg = 0.5kx^2

The Attempt at a Solution


I tried using the first equation and got x = 0.1m as my ans. which was wrong. I then tried using the second equation instead and still got an incorrect answer. Where am I going wrong? The ans. is 0.2 m.

Thanks in advance!
 
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  • #2
You need to look at this problem from an energy conservation standpoint.
 
  • #3
The block comes to a stop when its speed is zero. Your approach is invalid because the speed of the block is not necessarily zero when the net force acting on the block is zero.
 
  • #4
Hmm ok would it be something like this? mgh = 0.5kx^2 and the x and the h are the same? Cuz then solving for h I get (2mg)/k and when I subbed in the number I got 0.2. Is this the right way of doing this problem?
 
  • #5
Looks like a good way to get the answer!
 
  • #6
Your answer is correct; however, it is important you understand why the approach is valid. Do you?
 

1. How does the mass of the block affect its movement?

The mass of the block directly affects the amount of force needed to move it, as well as the amplitude and frequency of its oscillations. Heavier blocks will require more force to move and will have larger amplitudes and longer periods of oscillation compared to lighter blocks.

2. What is the relationship between the spring constant and the displacement of the block?

The displacement of the block is directly proportional to the spring constant, meaning that as the spring constant increases, the displacement of the block will also increase. This is because a higher spring constant indicates a stiffer spring, which will require more force to compress or stretch, resulting in a larger displacement of the block.

3. How does the initial position of the block affect its movement?

The initial position of the block affects the amplitude and phase of its oscillations. If the block is initially at rest, it will have a maximum displacement at the equilibrium point. However, if the block is initially displaced from the equilibrium point, it will have a smaller amplitude and a phase shift in its oscillations.

4. What is the relationship between the spring constant and the period of oscillation?

The period of oscillation is inversely proportional to the square root of the spring constant. This means that as the spring constant increases, the period of oscillation will decrease, resulting in faster oscillations of the block.

5. How does the amplitude of the block's oscillations change over time?

The amplitude of the block's oscillations will decrease over time due to the dissipation of energy through friction and air resistance. This phenomenon is known as damping and can be calculated using the block's mass, spring constant, and damping coefficient.

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