Please include steps A block of mass 1.4 kg is attached to a horizontal spring t

Question

Please include steps

A block of mass 1.4 kg is attached to a horizontal spring that has a force constant 1 100 N/m as shown in the figure below. The spring is compressed 2.0 cm and is then released from rest.

(a) A constant friction force of 3.6 N retards the block's motion from the moment it is released. Using an energy approach, find the position x of the block at which its speed is a maximum.
cm
(b) Explore the effect of an increased friction force of 13.5 N. At what position of the block does its maximum speed occur in this situation?
cm

Explanation / Answer

So first find the total energy which will be the potential intially

ET=EP0=.5kx2=.5(1100)(-.02)2=.22J

Because is cannot be destroyed we can say

ET-Wfriction = EP+Ek

.22-3.6(x+.02)=.5(1100)x2+.5(1.4)v2

Solving for v

v=(-.102857-5.1428x-785.714x2)

I graphed this on my calculator and used and foudn the max position to be

-.003274 where 0 is where the spring is unstretched and it is compressed in the negative direction (started at -.02)

If you replace 3.6 by 13.5 you find the new max to occur when x=-.0122726

Hopes that helps

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