You attach one end of a spring with a force constant k = 753 N/m to a wall and t

Question

You attach one end of a spring with a force constant k = 753 N/m to a wall and the other end to a mass m = 1.82 kg and set the mass-spring system into oscillation on a horizontal frictionless surface as shown in the figure. To put the system into oscillation, you pull the block to a position xi = 7.16 cm from equilibrium and release it. A horizontal spring labeled k is attached on its left end to the base of a wall, and on its right end to a block labeled m that rests upon the floor. There are three points along the floor that are labeled. The first point is near the middle of the apparatus, and is marked x=0. To the right of that point is a point marked x=x_i/4. Directly under the block is a point marked x=x_i. (a) Determine the potential energy stored in the spring before the block is released. Correct: Your answer is correct. J (b) Determine the speed of the block as it passes through the equilibrium position. Correct: Your answer is correct. m/s (c) Determine the speed of the block when it is at a position xi/4. Incorrect: Your answer is incorrect. Is energy conserved for this oscillating block-spring system? m/s

I need part C in detail.

Explanation / Answer

a) 0.5*753*0.0716*0.0716 = 1.93 J

b)1.93 =0.5*1.82*v*v
v= 2.302 m/s

c)

0.5*753*(0.0716^2 - 0.0179^2 ) = 0.5*753*v*v

v = 0.069 m/s

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