How Far Does a Block Slide When Launched by a Compressed Spring?

In summary, the block slides 14987.75 cm if the coefficient of sliding friction between the block and the surface is 0.25.
  • #1
warmfire540
53
0
A spring of spring constant k = 340 Nm-1 is used to launch a 1.5-kg block along a horizontal surface by compressing the spring by a distance of 18 cm. If the coefficient of sliding friction between the block and the surface is 0.25, how far does the block slide?

Well i have:

W=1/2kx^2
W=55080J
W=U(potential energy) so i know the potential energy of the spring is 55080
Energy is conserved..so after the spring has decompressed all the energy is in the block..which is now kinetic
K=1/2mv^2
55080=1/2(1.5)v^2
so Vi=406.5m/s ?? that seems pretty darn high, this is just the initial velocity right?
so Vf=0
friction = 3.7N
F=ma
Vf^2=vi^2+2ax

I assume I'm using these equations..but am not sure how i arise to get accel or if I'm on the right track..
 
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  • #2
The spring constant is given in Nm-1 so you have to convert the length of the spring to
meters. you also multiplied by the mass (1.5kg) when you should have divided when calculating Vi.
Calculating the speed of the block is really unnecessary, because you can do it all with potential energy. All of the potential energy of the spring will go to friction. Since the friction force is constant and in the opposite direction of the velocity. The energy dissipated by friction is Force * distance.
(using a rounded off value of 3.7N in your calculations could make the final answer wrong)
 
  • #3
kamerling said:
The spring constant is given in Nm-1 so you have to convert the length of the spring to
meters. you also multiplied by the mass (1.5kg) when you should have divided when calculating Vi.
Calculating the speed of the block is really unnecessary, because you can do it all with potential energy. All of the potential energy of the spring will go to friction. Since the friction force is constant and in the opposite direction of the velocity. The energy dissipated by friction is Force * distance.
(using a rounded off value of 3.7N in your calculations could make the final answer wrong)


well..friction is 3.675N
So, i know the potential energy of the spring is 55080J, how would i set up an equation to figure out the distance the block would travel?
 
  • #4
Hint: All the initial energy ends up dissipated by friction. What work is done by the friction force?
 
  • #5
Doc Al said:
Hint: All the initial energy ends up dissipated by friction. What work is done by the friction force?

The work of friction (Wf) is:
W=Fx
so Wf=3.675x
 
  • #6
warmfire540 said:
The work of friction (Wf) is:
W=Fx
so Wf=3.675x
Good. Keep going.
 
  • #7
the work of the spring (potential energy) (using the work-energy theorem) is 55080...
so 55080=3.675x
x=14987.75?
that can't be right..i must be missing a step?
 
  • #8
warmfire540 said:
the work of the spring (potential energy) (using the work-energy theorem) is 55080...
Redo this calculation, paying attention to units. (Convert cm to m.)
so 55080=3.675x
x=14987.75?
that can't be right..i must be missing a step?
Once you correct your value for spring PE you should be fine. I don't see any missing steps. (Calculating KE at intermediate points is unecessary.)
 
  • #9
Doc Al said:
Redo this calculation, paying attention to units. (Convert cm to m.)

Once you correct your value for spring PE you should be fine. I don't see any missing steps. (Calculating KE at intermediate points is unecessary.)



BLAGH!
stupid mistake on my part...
so work now is equal to 5.5J
so 5.5=3.675x
x=1.49m

answer to the problem..
 

Related to How Far Does a Block Slide When Launched by a Compressed Spring?

1. How does a spring push a block?

A spring pushes a block by exerting a force on the block due to its elastic potential energy. When the spring is compressed, it stores potential energy which is released when the spring expands, pushing the block in the opposite direction.

2. What factors affect the force of a spring pushing a block?

The force of a spring pushing a block is affected by the spring constant, which is a measure of the stiffness of the spring. It is also affected by the distance the spring is compressed or stretched, and the mass of the block.

3. Can a spring push a block with a constant force?

No, the force of a spring pushing a block is not constant. It follows Hooke's Law, which states that the force exerted by a spring is directly proportional to the distance it is compressed or stretched.

4. How does the surface of the block affect the force of a spring?

The surface of the block can affect the force of a spring by providing more or less friction. If the surface is smooth, there will be less friction and the spring will be able to push the block with more force. If the surface is rough, there will be more friction and the spring will have to exert more force to push the block.

5. What is the relationship between the force of a spring and the displacement of the block?

The force of a spring pushing a block is directly proportional to the displacement of the block from its equilibrium position. This means that the further the block is from its resting position, the greater the force the spring will exert on it.

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