Spring Potential energy, should be easy?

In summary, a spring with a spring constant of 500 N/m is used to propel a 0.42-kg mass up an inclined plane, which is 3 m long and inclined at 32°. The spring is compressed 30 cm and launches the mass onto the plane from rest. Both the plane and the horizontal surface have a coefficient of kinetic friction with the mass of 0.35. When the spring is compressed, the mass is at a distance of 1.6 m from the bottom of the plane. To find the speed of the mass, the work done by friction must be subtracted from the initial mechanical energy, which consists of the elastic potential energy of the compressed spring. Using
  • #1
Patdon10
85
0

Homework Statement



A spring with a spring constant of 500 N/m is used to propel a 0.42-kg mass up an inclined plane. The spring is compressed 30 cm from its equilibrium position and launches the mass from rest across a horizontal surface and onto the plane. The plane has a length l = 3 m and is inclined at 32°. Both the plane and the horizontal surface have a coefficient of kinetic friction with the mass of 0.35. When the spring is compressed, the mass is at distance d = 1.6 m from the bottom of the plane.

6-p-057-alt.gif



(a) What is the speed of the mass as it reaches the bottom of the plane?
1Your answer is incorrect.

(b) What is the speed of the mass as it reaches the top of the plane?
2

(c) What is the total work done by friction from the beginning to the end of the mass's motion?


Homework Equations



E = K + PE
Ki + PEi = Kf PEf
Elastic Potential Energy = (1/2)kx2

The Attempt at a Solution



I'm pretty sure I can solve this fairly easily after I figure out part A. However, Part A is giving me a lot of trouble.

K_i + Elastic PE_i = K_f + Elastic PE_f
0 + (1/2)(500)(1.62) = (1/2)(0.42)(v2) + 0
v = 55.205 m/s

That's wrong, any advice?

Thanks in advance.
 
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  • #2
Patdon10 said:
K_i + Elastic PE_i = K_f + Elastic PE_f
0 + (1/2)(500)(1.62) = (1/2)(0.42)(v2) + 0
v = 55.205 m/s
(1) You forgot about friction! (What's the work done by friction?)
(2) The compression of the spring is not 1.6 m.
 
  • #3
Doc Al said:
(1) You forgot about friction! (What's the work done by friction?)
(2) The compression of the spring is not 1.6 m.

The work done by friction is the Frictional force multiplied by the distance. Would calculating that work value help me find the velocity. I remembered I had a bigger problem trying to figure out this problem that I forgot to include in the 'attempt at a solution'.

This is what I've got:
I have an initial elastic potential energy, and a final kinetic energy. With the givens, I can also calculate the force of friction on the block, but how do I incorporate that into the equation?
Even if I can find a force from the spring, I could use Newton's 2nd law to find the final speed.

Any insight?
 
  • #4
Patdon10 said:
I have an initial elastic potential energy, and a final kinetic energy. With the givens, I can also calculate the force of friction on the block, but how do I incorporate that into the equation?
Initial mechanical energy - work done by friction = final mechanical energy

The work done by friction is negative work: it decreases the mechanical energy.

What's the work done by friction? Incorporate that into your energy balance as I indicate above.
 
  • #5
Ok, so let's try this again:
Work done by friciton is:
F_fr = mgμ = (0.42)(9.81)(0.35) = 1.44 N
W_fr = (1.44N)(1.6m) = 2.307 Nm

0 + (1/2)(500N/m)(0.3m^2) - 2.307 Nm = (1/2)(0.42)(v^2) + 0
22.5 - 2.307 = 0.21v^2
v = 9.806 m/s

Which is exactly right! Thank you so much. I wish I would have thought to put it into a work equation. I need to pay more attention to the units to see that I can do things like that. From here on out, I should be able to just use kinematics
 

Related to Spring Potential energy, should be easy?

1. What is spring potential energy?

Spring potential energy is the potential energy stored in a spring when it is stretched or compressed. It is a type of elastic potential energy, meaning it is the energy stored in an object due to its deformation.

2. How is spring potential energy calculated?

The formula for calculating spring potential energy is PE = 1/2 kx^2, where k is the spring constant and x is the displacement of the spring from its equilibrium position. The spring constant represents the stiffness of the spring, while the displacement is the distance the spring has been stretched or compressed.

3. What factors affect spring potential energy?

The amount of spring potential energy stored in a spring depends on the stiffness of the spring (determined by the spring constant) and the amount of displacement. A stiffer spring or a larger displacement will result in more potential energy stored.

4. What is the difference between spring potential energy and spring constant?

Spring potential energy is the energy stored in a spring, while the spring constant is a physical quantity that represents the stiffness of the spring. Spring potential energy is dependent on the spring constant, but they are not the same thing.

5. How is spring potential energy used in everyday life?

Spring potential energy is used in many everyday objects, such as trampolines, pogo sticks, and door hinges. It is also used in various technologies, such as shock absorbers, to help absorb and release energy in a controlled manner.

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