A block is placed on top of a vertical spring, and the spring compresses. The fi

Question

A block is placed on top of a vertical spring, and the spring compresses. The figure below depicts a moment in time when the spring is compressed by an amount h.

(a) To calculate the change in the gravitational and elastic potential energies, what must be included in the system? (Select all that apply.)

the Sunspringthe Earthairblockfriction from the floor

(b) Find an expression for the change in the system's potential energy in terms of the parameters shown in the figure. (Use any variable or symbol stated above along with the following as necessary: g. Do not substitute numerical values; use variables only.)


(c) If

m = 0.750 kg

and

k = 150 N/m

, find the change in the system's potential energy when the block's displacement is

h = 0.0625 m,

relative to its initial position.
J

Explanation / Answer

A.

Spring [ANSWER, for elastic potential energy]
The block [ANSWER, for gravitational potential energy]
The Earth [ANSWER, for gravitational potential energy]

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B.

Initially,we set that the block is at y = h. Here, the spring is uncompressed. Thus,

Ui = m g h

Now, after compression, the spring is compressed by an amount h, and the block is not at y = 0.

Thus,

Uf = 1/2 k h^2

Thus, the change in potential energy is

Uf - Ui = 1/2 k h^2 - m g h [ANSWER]

****************************

Using the expression from B, substituting values,

Uf - Ui = -0.1664 J [ANSWER]

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