Using the Work-Energy Theorem to Solve a Textbook Sliding Problem with Friction

In summary: Remember that the work done by the spring is negative. In summary, using the work-energy theorem, we can find how far a 2.50-kg textbook, compressed against a spring with a force constant of 250N/m and released on a horizontal table with a coefficient of kinetic friction of 0.30, moves from its initial position before coming to rest. By considering the work done by friction and the change in kinetic energy, we can determine that the change in kinetic energy is zero and the work done by the spring is equal to the work done by friction. This allows us to solve for the distance traveled by the textbook before it comes to rest.
  • #1
Yosty22
185
4

Homework Statement



A 2.50-kg textbook is forced against a horizontal spring of negligible mass and force constant, k, of 250N/m, compressing the spring a distance of 0.250 m. When released, the textbook slides on a horizontal tabletop with coefficient of kinetic friction μk=0.30. Use the work-energy theorem to find how far the text-book moves from its initial position before coming to rest.

Homework Equations



Wtot=K2-K1=ΔK (work-energy theorem)
K=0.5mv2

The Attempt at a Solution



I have no idea how to even start. It says that I have to use the work energy theorem, so all I can think of doing is substitution. However, Work-energy theorem has no reference to kinetic friction, just kinetic energy. Any ideas to get me started?
 
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  • #2
Yosty22 said:
However, Work-energy theorem has no reference to kinetic friction, just kinetic energy. Any ideas to get me started?
Friction is a force, so consider the work done by it.
 
  • #3
Doc Al said:
Friction is a force, so consider the work done by it.

Ok, so I used the equation friction=μ*n.

Since the table it is on is horizontal, that means that there is no acceleration or any motion up or down, so W=N. In this case, I use the weight of the box which came out to be 9.8*2.5=24.5N.

I found the force of force of friction to be 7.35N acting in the opposite direction of motion. This is where I am stuck. If I put Work due to friction in the work energy theorem, I have to multiply the force of friction by the distance over which it acts. How do I find the distance that the friction acts over? I thought that the force of friction acted over the same distance as it moved, just in the opposite direction. In this case, I still have two unknowns: the total distance that the block traveled and its velocity, but the problem only asks for the distance. How would I go about finding the velocity if it is not given and I don't know the kenetic energy or how far it traveled or any time interval?
 
  • #4
Hint: What's final speed of the book?
 
  • #5
Doc Al said:
Hint: What's final speed of the book?

Ahh, ok, it would be zero becuase it comes to a rest. However, wouldn't it start from rest as well, since it is pushed up against the compressed spring? Or would I designate v1to be the moment it leaves the spring?
 
  • #6
Yosty22 said:
Ahh, ok, it would be zero becuase it comes to a rest. However, wouldn't it start from rest as well, since it is pushed up against the compressed spring?
Yes, it starts from rest and ends up at rest.
Or would I designate v1to be the moment it leaves the spring?
All you need to worry about is the change in KE. What would that be? (No need to worry about intermediate points.)
 
  • #7
So wouldn't that mean the change is 0? In which case, there is no kinetic energy. Does that make sense?
 
  • #8
Yosty22 said:
So wouldn't that mean the change is 0? In which case, there is no kinetic energy. Does that make sense?
The change in kinetic energy is zero, which makes perfect sense. After all, you're trying to find how how far the thing goes before friction brings it to rest. (That doesn't mean that there wasn't kinetic energy while it was moving, but who cares?)
 
  • #9
So since friction and the spring are both doing work, would the total work be the (work of the spring) - (the work of friction) since work by friction is against motion?
 
  • #10
Sydney Austin said:
So since friction and the spring are both doing work, would the total work be the (work of the spring) - (the work of friction) since work by friction is against motion?
Sure.
 

1. What is the Work-Energy Theorem?

The Work-Energy Theorem is a principle in physics that relates the work done on an object to the change in its kinetic energy. It states that the net work done on an object is equal to the change in its kinetic energy.

2. How is the Work-Energy Theorem applied in problem solving?

In problems involving the Work-Energy Theorem, one must identify the initial and final states of the object, calculate the work done on the object by all forces, and then equate that to the change in the object's kinetic energy.

3. Can the Work-Energy Theorem be used for all types of forces?

Yes, the Work-Energy Theorem can be applied to all types of forces, including conservative and non-conservative forces. However, for non-conservative forces, the work done must be calculated using the integral of force over displacement.

4. What are the units of work and kinetic energy?

The units of work are joules (J), which is equivalent to a Newton-meter (N*m). The units of kinetic energy are also joules (J), as it is a form of energy.

5. Are there any limitations to the application of the Work-Energy Theorem?

The Work-Energy Theorem assumes that there are no external forces acting on the object, and that the object is moving in a straight line. Additionally, it does not account for changes in potential energy or work done by friction. Therefore, it may not accurately predict the motion of an object in all situations.

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