How Far Will the Spring Stretch Beyond Equilibrium in Its First Swing?

In summary, the conversation is about a problem involving a wood block attached to a horizontal spring and its movement on a table with friction. The question is how far the spring will stretch beyond its equilibrium when released from a compressed position. The solution involves using the conservation of energy approach and answering questions about the potential energy of the mass on the spring, work done by friction, and the spring constant.
  • #1
Joyce
1
0
Spring Equilibrium -- Need help! :(

Hi i have this question:

A 200 g wood block is firmly attached to a horizontal spring. The block can slide along a tbale where the coefficient of friction is 0.40. A force of 10 N compresses the string 18 cm. If the spring is released from this position, how far beyond its equilibrium will it stretch in its first swing?

Does anyone think they can help me get started on this cause I'm pretty clueless!

thx!
 
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  • #2
try using a conservation of energy aproach.

[tex] KE_i + PE_i + W = KE_f + PE_f [/tex]

Some questions that you will need to answer before you do this:
1) What is the equation for the potential energy of a mass on a spring?
2) What is the equation for the work done by friction as the block moves along the table?
3) What is the definition of the spring constant (k)?
 
  • #3


Hi there,

Sure, I can try to help you with this question. Let's break it down step by step.

First, we need to understand what is meant by "equilibrium". In physics, equilibrium refers to a state where all forces acting on an object are balanced, resulting in no acceleration. In this case, we are looking for the equilibrium position of the spring, where the force from the spring is equal and opposite to the force from gravity.

Next, we need to use the information given to us. We know that the block has a mass of 200 g, the coefficient of friction is 0.40, and the force applied to compress the spring is 10 N. We also know that the spring is compressed 18 cm.

We can start by finding the force from gravity acting on the block. This can be calculated using the formula F = mg, where m is the mass and g is the acceleration due to gravity (9.8 m/s^2). In this case, the force from gravity is 0.2 kg x 9.8 m/s^2 = 1.96 N.

Now, let's consider the forces acting on the spring. We have the force from gravity pulling the block down, and the force from the spring pushing the block up. The force from the spring can be calculated using Hooke's law, F = kx, where k is the spring constant and x is the displacement from the equilibrium position. We can rearrange this equation to solve for x, which gives us x = F/k. We know that the force from the spring is 10 N and we can find the spring constant by using the given information that the spring is compressed 18 cm. We can convert this to meters (0.18 m) and use the equation k = F/x. This gives us a spring constant of 55.56 N/m.

Now, we can use this spring constant to find the equilibrium position of the spring. Since we know that the force from the spring is equal and opposite to the force from gravity, we can set these two forces equal to each other: Fg = Fs. This gives us the equation mg = kx. Plugging in the values we know, we get 0.2 kg x 9.8 m/s^2 = 55.56 N/m x x. Solving for x, we get x = 0.035 m or 3.
 

Related to How Far Will the Spring Stretch Beyond Equilibrium in Its First Swing?

What is "Spring Equilibrium"?

"Spring Equilibrium" refers to the time of year when the length of day and night are approximately equal. This occurs twice a year, in the spring and fall, and marks the official beginning of the spring season.

What causes the Spring Equilibrium?

The Spring Equilibrium is caused by the tilt of the Earth's axis and its orbit around the sun. As the Earth rotates around the sun, the tilt of its axis causes different parts of the planet to receive varying amounts of sunlight, resulting in the changing of the seasons.

When does the Spring Equilibrium occur?

The Spring Equilibrium occurs on March 20th or 21st in the Northern Hemisphere, and September 22nd or 23rd in the Southern Hemisphere.

Why is the Spring Equilibrium important?

The Spring Equilibrium is significant because it marks the official beginning of the spring season. It also has cultural and religious significance for many societies around the world.

How can I observe the Spring Equilibrium?

The easiest way to observe the Spring Equilibrium is by looking at the length of day and night on March 20th or 21st. They should be nearly equal in length, with approximately 12 hours of daylight and 12 hours of darkness.

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