What is the speed of a block pulled by a spring with friction?

In summary, a block with a mass of 1.50 kg, attached to a spring with a force constant of 456.0 N/m, is pulled 3.60 cm to the right of its equilibrium position and released from rest. The coefficient of kinetic friction between the block and the surface is 0.210. Using the equation W=Ef-Ei and accounting for the negative work done by friction, the correct answer for the speed of the block as it passes by its equilibrium position is 0.496 m/s.
  • #1
alexpratt
18
0

Homework Statement



A block with mass 1.50 kg is attached as shown to a spring with a force constant of 456.0 N/m. The coefficient of kinetic friction between the block and the surface on which it slides is 0.210. The block is pulled 3.60 cm to the right of its equilibrium position and then released from rest. What is the speed of the block as it passes by its equilibrium position?

Homework Equations



W=Ef-Ei

The Attempt at a Solution



W is the work done by friction, which would be f*d, where f is coefficient of friction and d is the distance the block is pulled back.
Ef is the final energy which would be the kinetic energy of the block minus the force of the spring since the spring is pushing on the block, however since I am looking at the equilibrium as my final position I am assuming this is 0?
Ei is the initial energy which is the kinetic energy minus the energy of the spring, but there's no velocity so kinetic energy is 0.


so i have my equation as

f*d=Ke(final)-Se(initial)
f*d=1/2mv^2 - 1/2kd^2

when i solve for v i get .636m/s which is incorrect.
i goofed up the equation somewhere, can anyone help me?
 
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  • #2
alexpratt said:

Homework Statement



A block with mass 1.50 kg is attached as shown to a spring with a force constant of 456.0 N/m. The coefficient of kinetic friction between the block and the surface on which it slides is 0.210. The block is pulled 3.60 cm to the right of its equilibrium position and then released from rest. What is the speed of the block as it passes by its equilibrium position?

Homework Equations



W=Ef-Ei

The Attempt at a Solution



W is the work done by friction, which would be f*d, where f is coefficient of friction and d is the distance the block is pulled back.
The work done by friction is (force of friction) (d), where the friction force is not the coefficient of friction. Friction force = ____?
Ef is the final energy which would be the kinetic energy of the block minus the force of the spring since the spring is pushing on the block, however since I am looking at the equilibrium as my final position I am assuming this is 0?
Ei is the initial energy which is the kinetic energy minus the energy of the spring, but there's no velocity so kinetic energy is 0.


so i have my equation as

f*d=Ke(final)-Se(initial)
f*d=1/2mv^2 - 1/2kd^2

when i solve for v i get .636m/s which is incorrect.
i goofed up the equation somewhere, can anyone help me?
The equation is OK, except correct the value of 'f'.
 
  • #3
ok, so its f*mg*d? when i do that i get 0.737, last time i checked anyways. So maybe my math is off.
 
  • #4
The work done by friction is negative...the force is opposiote to the direction of displacement, hence negative...watch that minus sign...it bites every time, if given the chance.:wink:
 
Last edited:
  • #5
ahh, thank you! Got the answer to be 0.496 m/s, i almost ran out of tries too!
 

1. What is the work-energy theorem?

The work-energy theorem is a principle in physics that states that the work done on an object is equal to the change in its kinetic energy.

2. How is the work-energy theorem applied in real-life situations?

The work-energy theorem can be applied in various real-life situations, such as calculating the amount of work needed to lift an object, determining the speed of a moving vehicle, or understanding the energy transfer in a roller coaster ride.

3. What is the formula for the work-energy theorem?

The formula for the work-energy theorem is W = ΔKE, where W represents work, and ΔKE represents the change in kinetic energy.

4. How is the work-energy theorem related to the law of conservation of energy?

The work-energy theorem is closely related to the law of conservation of energy. The work done on an object results in a change in its kinetic energy, which is a form of energy. This change in kinetic energy can be accounted for by the conservation of energy principle, which states that energy cannot be created or destroyed, only transferred or transformed.

5. Can the work-energy theorem be applied to non-conservative forces?

No, the work-energy theorem can only be applied to conservative forces, where the work done is independent of the path taken. For non-conservative forces, the work done will depend on the path taken, and the work-energy theorem cannot be used.

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