The spring connects two objects. In this case, it's the object that moves and accelerates, and the wall. I will take x to be the distance from the particle to the wall -- the length of the spring. The problem is one-dimensional. (There are two- and three-dimensional forms of the problem.) The ideal spring exerts a force (F) on the object, with the following properties:The spring has a length (ℓ) where it exerts no force. (I usually call it the relaxed length. I might call it the "zero-force length" or the "equilibrium length".)The compressed spring pushes. The stretched string pulls. The force on the block is F = -k(x - ℓ). (Figure out what the negative sign on k does.)Often, people use x for the difference from equilibrium, and write F = -kx instead.Sometimes, both sides of the spring are at different positions. The force on the object on the right side is -k(x2 - x1 - ℓ). In the pictured situation, x1 = 0 and x2 = x.Understand what is physically happening with the spring -- the ideal version, and differences from ideal.Question: if k = 29 N/cm, ℓ = 9 cm, and x = 12 cm, calculate the force (in Newtons) on the object, including the sign to indicate the direction.

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Description: The spring connects two objects. In this case, it's the object that moves and accelerates, and the wall. I will take x to be the distance from the particle to the wall -- the length of the spring. The problem is one-dimensional. (There are two- a

The force exerted by the spring on the object is proportional to the displacement (compression or…

Answered: if k = 29 N/cm, ℓ = 9 cm, and x = 12…

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The spring connects two objects. In this case, it's the object that moves and accelerates, and the wall. I will take x to be the distance from the particle to the wall -- the length of the spring. The problem is one-dimensional. (There are two- and three-dimensional forms of the problem.)

The ideal spring exerts a force (F) on the object, with the following properties:

The spring has a length (ℓ) where it exerts no force. (I usually call it the relaxed length. I might call it the "zero-force length" or the "equilibrium length".)
The compressed spring pushes. The stretched string pulls. The force on the block is F = -k(x - ℓ). (Figure out what the negative sign on k does.)
Often, people use x for the difference from equilibrium, and write F = -kx instead.
Sometimes, both sides of the spring are at different positions. The force on the object on the right side is -k(x₂ - x₁ - ℓ). In the pictured situation, x₁ = 0 and x₂ = x.

Understand what is physically happening with the spring -- the ideal version, and differences from ideal.

Question: if k = 29 N/cm, ℓ = 9 cm, and x = 12 cm, calculate the force (in Newtons) on the object, including the sign to indicate the direction.

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