The potential energy of an interaction is given by U ( x )= a x 2,where a = +6.4

Question

The potential energy of an interaction is given by U(x)=ax2,where a = +6.4 J/m2. Initial speed of a 0.76-kg object in this system is 2.68 m/s atx = 0.

Part A

How far does the object travel before it reaches a speed of v = 0?

Express your answer with the appropriate units.

S = ?

Part B

Does your answer in the previous part depend on whether the object is traveling in the positive or negative x direction?

No, it does not depend on whether the object is traveling in the positive or negative xdirection. Yes, the answer in the previous part is for the object traveling in the negative x direction, the distance for the object traveling in the positive x direction is greater than the obtained result. Yes, the answer in the previous part is for the object traveling in the positive x direction, the distance for the object traveling in the negative x direction is greater than the obtained result.

Explanation / Answer

Here ,

U = ax^2

U = 6.4 x^2

a) let the position of particle is x when the velocity is zero

using coseravtion of energy

initial mechanical energy = final mechanical energy

0.5 * 0.76 * 2.68^2 = 6.4 * x^2

solving for x

x = 0.653 m

the object travels 0.653 m before it stops

B)

as the potential energy is an even function

No, it does not depend on whether the object is traveling in the positive or negative xdirection.

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