Principle of work and energy to a collar and spring system, been stuck for hours

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Homework Help Overview

The problem involves a collar and spring system where a collar is released from rest and travels downward, requiring the determination of the average friction force exerted on the collar. The context includes parameters such as mass, spring constant, and distances related to gravitational potential energy and spring displacement.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculation of spring displacement and its relevance to the energy equation. There is a focus on the difference between initial and final states of the spring and how this affects the energy stored in the spring.

Discussion Status

Participants are actively questioning the assumptions regarding spring displacement and energy calculations. Some guidance has been offered regarding the treatment of initial elastic energy, but there is no explicit consensus on the correct approach to the problem.

Contextual Notes

There are indications of confusion regarding the unstretched length of the spring and how it relates to the energy calculations. The problem setup includes specific values and conditions that may influence the interpretation of the spring's energy state.

engineering810
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Homework Statement


I've been attempting this problem all day now. My current submissions are 10.6N and I keep getting 7.04N every time I retry it but this is also wrong. Can somebody please help me out so I can figure out what I'm doing wrong? Thanks for any help in advanced!

The 3.35kg collar shown below is attached to a spring and released from rest at A. The collar then travels downward a distance of y = 2.00m . The spring has a spring constant of k = 22.5N/m . The distance a is given as 1.15m . The datum for gravitational potential energy is set at the horizontal line through A and B.

Determine the magnitude of the average friction force exerted on the collar when the velocity of the collar at C is 3.52m/s and the spring has an unstretched length of 0.65m .
Express your answer to three significant figures and include the appropriate units.
14.6.jpg


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Homework Equations



mgy = YF+(1/2)mv^2+(1/2)kx^2

F = frictional force

The Attempt at a Solution


(3.35)*(9.81)*(2) = 2F + (0.5)*(3.35)*(3.52^2) + (0.5)*(22.5)*(1.657^2)
65.727 = 2F + 20.7539 + 30.8886
65.727 = 2F + 51.6425
2F = 14.08
F = 7.04 Newtons
 
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The spring displacement is wrong. Displacement is the difference between initial and final state.
 
jack action said:
The spring displacement is wrong. Displacement is the difference between initial and final state.
Yea but unstretched is still 0.65. It starts at 1.15 but isn't unstretched at 1.15
 
It doesn't matter. The only energy added to the spring is done between initial and final state. The energy stored within the 0.65 and 1.15 was already in the spring at the initial state and is still in the spring at the final state.
 
engineering810 said:
Yea but unstretched is still 0.65. It starts at 1.15 but isn't unstretched at 1.15
The spring contained some elastic energy before the collar was released, this should be deducted from the elastic energy figure appearing in your equation.
 

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