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

In summary, the conversation discusses a physics problem involving a collar attached to a spring and released from rest. The problem involves finding the magnitude of the average friction force exerted on the collar when it reaches a certain velocity and the spring has an unstretched length. The main equation used is mgy = YF+(1/2)mv^2+(1/2)kx^2. The conversation also includes a discussion about the correct displacement of the spring.
  • #1
engineering810
7
0

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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  • #2
The spring displacement is wrong. Displacement is the difference between initial and final state.
 
  • #3
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
 
  • #4
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.
 
  • #5
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.
 

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

1. What is the principle of work and energy?

The principle of work and energy states that the work done on an object is equal to the change in its kinetic energy. In other words, work is the transfer of energy from one form to another.

2. How does the principle of work and energy apply to a collar and spring system?

In a collar and spring system, work is done by the force of the spring on the collar as it is compressed or stretched. This work is then stored as potential energy in the spring. As the collar moves, this potential energy is converted into kinetic energy, according to the principle of work and energy.

3. Why would a collar and spring system get stuck?

A collar and spring system can get stuck if there is too much friction between the collar and the surface it is moving on, or if the spring is too strong and cannot be compressed or stretched easily. Additionally, external forces such as gravity or other objects can also cause the system to get stuck.

4. How can the principle of work and energy be used to free a stuck collar and spring system?

If the collar and spring system is stuck due to excess friction, the principle of work and energy can be used to calculate the minimum amount of force needed to overcome the friction and move the collar. If the system is stuck due to a strong spring, the principle can be used to determine the amount of force needed to compress or stretch the spring enough to free the collar.

5. How can the principle of work and energy be applied to real-world situations?

The principle of work and energy is a fundamental concept in physics and can be applied to various real-world situations, such as calculating the energy needed to launch a rocket into space or determining the force needed to move a heavy object. It is also used in the design of machines and mechanical systems to ensure efficient use of energy and minimize friction.

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