Spring problem using work energy theorem

In summary, a 2.90 kg block attached to a horizontal spring with force constant 860 N/m and compressed 0.0360 m is released from rest on a horizontal floor with a coefficient of kinetic friction of 0.35. The block slides along the floor and the spring is compressed 0.0160 m when the block has moved a distance of 0.0200 m. Using the equation Work=Eb-Ea, where Eb is the final kinetic and potential energy and Ea is the initial kinetic and potential energy, the speed of the block can be calculated. The work done by friction is negative and the final answer is 0.414.
  • #1
Garrit
6
0

Homework Statement


A 2.90 kg block on a horizontal floor is attached to a horizontal spring that is initially compressed 0.0360 m . The spring has force constant 860 N/m . The coefficient of kinetic friction between the floor and the block is 0.35 . The block and spring are released from rest and the block slides along the floor.

What is the speed of the block when it has moved a distance of 0.0200 m from its initial position? (At this point the spring is compressed 0.0160 m)

Homework Equations


I'm using the equation Work( of the nonconservative forces) = Eb - Ea where Eb equals the final kinetic energy plus the final potential energy and Ea equals the initial kinetic energy plus the initial potential energy. I'm calculating kinetic energy using (1/2)mv^2 and for potential energy (1/2)kx^2.

The Attempt at a Solution


My attempt at it:

The work done by friction should equal (mass)(gravity)(coefficient of friction)(displacement) which would equal 2.9(9.8)(0.35)(0.02)

Now for the other side of the equation:

(1/2)(m)vf^2 + (1/2)k(x2)^2 - ( (1/2)(m)vi^2 + 1/2k(x1)^2 )

So this is what I get:

2.9(9.8)(0.35)(0.02) = (1/2)(2.9)(vf)^2 + (1/2)(860)(0.016) - (1/2)(2.9)(0) - (1/2)(860)(0.036)

I punched this into wolfram and got 2. something. I know the answer is 0.414, so I must be doing something wrong. I'm just using the equation I learned in class. Any suggestions?
 
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  • #2
Is the work done by friction positive or negative?
 
  • #3
Garrit said:
The work done by friction should equal (mass)(gravity)(coefficient of friction)(displacement) which would equal 2.9(9.8)(0.35)(0.02)
So the friction is adding energy to the block?
 
  • #4
Ah so the work done by friction should be negative, right? That still doesn't give me 0.414 though. What else is wrong?
 
  • #5
Garrit said:
1/2k(x1)^2 )

Garrit said:
1/2)(860)(0.036)
Compare.
 
  • #6
ah man. Even writing out the equations, I still couldn't punch in the numbers right! Thanks so much guys. I made the corrections and got the answer I was looking for!
 

FAQ: Spring problem using work energy theorem

What is the "Spring problem using work energy theorem"?

The "Spring problem using work energy theorem" is a physics problem that involves a spring and an object attached to the spring. The problem requires the use of the work energy theorem, which states that the net work done on an object is equal to the change in its kinetic energy. This problem is commonly used to demonstrate the application of this principle in solving real-world scenarios.

What is the work energy theorem?

The work energy theorem is a fundamental principle in physics that states that the net work done on an object is equal to the change in its kinetic energy. This means that the total work done by all forces acting on an object is equal to the change in its speed or direction. It is often used to analyze the motion of objects and solve problems involving work and energy.

What is the role of a spring in the "Spring problem using work energy theorem"?

A spring is a flexible object that can be stretched or compressed by a force. In the "Spring problem using work energy theorem", the spring is used to store potential energy, which is then converted into kinetic energy as the spring returns to its original position. This allows for the application of the work energy theorem in solving the problem.

How do you solve a "Spring problem using work energy theorem"?

To solve a "Spring problem using work energy theorem", you first need to identify the initial and final positions of the object attached to the spring. Then, calculate the potential energy stored in the spring at the initial and final positions. Finally, use the work energy theorem formula to find the net work done on the object, which will be equal to the change in its kinetic energy.

What are some real-world applications of the "Spring problem using work energy theorem"?

The "Spring problem using work energy theorem" has many real-world applications, such as the design of shock absorbers in cars, the calculation of the force required to compress a spring in a mechanical system, and the analysis of the motion of objects attached to a spring, such as bungee jumpers or pogo sticks. It is also used in the study of elastic potential energy and the behavior of springs in various engineering and scientific fields.

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