Finding the distance a spring compresses

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In summary: So if the spring does no net work, then the object would only have to do the work of friction over the distance of 1.5*(d/2)?
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dal11
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Homework Statement



An object of mass m=2.2 kg is traveling on a horizontal surface. The coefficient of kinetic friction between the object and the surface is µk=0.2. The object has speed v=0.57 m/s when it reaches x=0 and encounters a spring. The object compresses the spring a distance d/2, stops instantaneously, and then travels back to x=0 where it stops completely. What is the total distance, d, that the object moves after first touching the spring?


Homework Equations



KE+Espring = KEi+Wfriction
Espring=.5k(x^2)
Fspring=kx

The Attempt at a Solution



I am really confused I don't think I have enough knowns to solve the problem.
 
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  • #2
dal11 said:

Homework Statement



An object of mass m=2.2 kg is traveling on a horizontal surface. The coefficient of kinetic friction between the object and the surface is µk=0.2. The object has speed v=0.57 m/s when it reaches x=0 and encounters a spring. The object compresses the spring a distance d/2, stops instantaneously, and then travels back to x=0 where it stops completely. What is the total distance, d, that the object moves after first touching the spring?


Homework Equations



KE+Espring = KEi+Wfriction
Espring=.5k(x^2)
Fspring=kx

The Attempt at a Solution



I am really confused I don't think I have enough knowns to solve the problem.

I think you may have more information than you realize.

You start with an initial KE at x = 0.

There are two sources of work against the mass from that point.

There is friction and the spring.

But the spring gains potential energy ... but then gives it back until the object it at rest just as it gets to x = 0 again. So how much net work did the spring do?
 
  • #3
0 I guess, I don't understand how that helps
 
  • #4
dal11 said:
0 I guess, I don't understand how that helps

If the spring does no net work in stopping the object doesn't all of the kinetic energy of the object need to be accounted for by just the friction over the distance of 2*(d/2) ?

Doesn't mv2/2 = Work of Friction = Ffriction * distance
 

1. How do you measure the distance a spring compresses?

To measure the distance a spring compresses, you will need a ruler or measuring tape. Place one end of the ruler at the base of the spring and measure to the top of the spring when it is at rest. Then, compress the spring and measure the new distance from the base to the top of the spring. The difference between the two measurements is the distance the spring has compressed.

2. What is the formula for calculating the distance a spring compresses?

The formula for calculating the distance a spring compresses is d = F / k, where d is the distance in meters, F is the force applied to the spring in Newtons, and k is the spring constant in N/m. This formula is known as Hooke's law.

3. How does the mass of an object affect the distance a spring compresses?

The mass of an object does not directly affect the distance a spring compresses. However, the force applied to the spring, which is dependent on the mass of the object and the gravitational acceleration, will affect the distance the spring compresses. Heavier objects will require more force to compress the spring, resulting in a larger distance of compression.

4. What factors can affect the accuracy of measuring the distance a spring compresses?

Several factors can affect the accuracy of measuring the distance a spring compresses. These include human error in reading the ruler or measuring tape, the precision of the ruler or measuring tape, and the elasticity of the spring. Other factors, such as external forces or temperature, may also affect the accuracy of the measurement.

5. How can the distance a spring compresses be used in real-world applications?

The distance a spring compresses is an important factor in many real-world applications, such as in shock absorbers for vehicles, springs in mattresses, and in various types of machinery. It is also used in physics experiments to study the relationship between force and distance in Hooke's law. Additionally, the distance a spring compresses can be used to determine the stiffness or spring constant of a spring, which is useful in engineering and design processes.

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