What did I miss in my energy and hook's law homework calculation?

In summary, a 205 g cube slides down a ramp with a 46° slope, falling 92 cm before striking a spring with a spring constant of 21 N/m. The maximum compression of the spring is found using the conservation of energy law, taking into account the work of friction, gravity, and the spring. The discrepancy between the attempt at the solution and the textbook answer may be due to a typo in the textbook.
  • #1
homo-sapiens
28
0

Homework Statement


A 205 g cube slides down a ramp starting from rest as shown in the figure below. The ramp has a 46° slope. After falling a distance of 92 cm, the cube strikes a spring of spring constant
k = 21 N/m.
Find the maximum compression of the spring when the coefficient of kinetic friction between the cube and the ramp is 0.13.
http://puu.sh/bTjhN/ed172bac4f.png [Broken]

2. Homework Equations

conservation of energy laws
f=ma

The Attempt at a Solution


I solved for work of friction, the work of gravity and the work of spring (d is vertical distance of 92cm and x is the distance of compression)[/B]
http://puu.sh/bTjoU/221afafc3f.png [Broken]

I then used the conservation of energy law to piece together my 3 equations
http://puu.sh/bTjw6/e9c0236b16.png [Broken]

apparently my equation didn't match with the answer's. Can someone please tell me why?? and what did I miss??
 
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  • #2
Looks OK to me - what was the model answer?
 
  • #3
Looks right to me also.
 
  • #4
http://puu.sh/bTRBF/53f9460841.jpg [Broken]
This is the textbook answer, could it be that the textbook is misprinted?
 

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  • #5
Probably a typo.
Either put a slash between μ and tan(θ) or change tan(θ) to cot(θ).
 

What is energy and how is it related to Hook's Law?

Energy is the ability to do work. It can take many forms, such as mechanical, thermal, electrical, or chemical. Hook's Law states that the force required to extend or compress a spring is directly proportional to the distance the spring is extended or compressed. This means that as the spring is stretched or compressed, it stores potential energy.

What is the formula for calculating potential energy in a spring?

The formula for calculating potential energy in a spring is PE = 1/2 * k * x^2, where PE is potential energy, k is the spring constant, and x is the distance the spring is compressed or extended.

How does Hook's Law apply to everyday objects?

Hook's Law applies to everyday objects because many objects, such as rubber bands, bungee cords, and car suspension systems, behave like springs. As these objects are stretched or compressed, they store potential energy and follow Hook's Law.

What happens to the potential energy in a spring when it is released?

When a spring is released, the potential energy stored in it is converted into kinetic energy as the spring returns to its original shape. This kinetic energy can then be transferred to other objects, causing them to move.

How does temperature affect the energy stored in a spring?

As temperature increases, the molecules in a spring vibrate more, causing the spring to expand and increasing its potential energy. This means that the spring constant, k, changes with temperature. Therefore, the potential energy stored in a spring can be affected by changes in temperature.

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