A block of mass 1.7 kg is attached to a horizontal spring that has a force const

Question

A block of mass 1.7 kg is attached to a horizontal spring that has a force constant 800 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 4.4 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.

(b) Explore the effect of an increased friction force of 10.5 N. At what position of the block does its maximum speed occur in this situation?

Explanation / Answer

a)Conserving energy,

0.5kA2=0.5k(A-x)2+0.5mv2+fx

0.16=400*(0.02-x)2+0.85v2+4.4x

0.85v2=0.16-4.4x-400*(0.02-x)2

Maximizing v2,

-4.4-800*(0.02-x)=0

x=0.0145m=1.45cm

b)Conserving energy for changed friction,

0.85v2=0.16-10.5x-400*(0.02-x)2

x=6.875*10-3m=0.6875cm

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