Consider the track shown in the figure. The section AB is one quadrant of a circ

Question

Consider the track shown in the figure. The section AB is one quadrant of a circle of radius 2.0 m and is frictionless. B to C is a horizontal span 3.4 m long with a coefficient of kinetic friction mu_k = 0-23. The section CD under the spring is frictionless. A block of mass 1.0 kg is released from rest at A. After sliding on the track, it compresses the spring by 0.20 m. (Figure 1) Part A Determine the velocity of the block at point B. Express your answer to two significant figures and include the appropriate units. Part B Determine the thermal energy produced as the block slides from B to C. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

(a) Determine the velocity of the block at point B.
(2*9.81*2) = 6.26 m/s

(b) Determine the work done by friction as the block slides from B to C.
0.23*1*9.81*3.4 = 7.67 J

(c) Determine the velocity of the block at point C.
[{(2/1)*{(0.5*1*6.26^2) - 7.67}] = 4.88 m/s

(d) Determine the stiffness constant k for the spring.
(4.88/0.20)^2= 596.2 N/m

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