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Consider the track shown in the Figure. The section AB is one quarter of a circl

ID: 2294596 • Letter: C

Question

Consider the track shown in the Figure. The section AB is one quarter of a circle of radius 2.00 m and is frictionless. B to C is a horizontal surface 3.50 m long with a coefficient of kinetic friction ?k = 0.250. The section CD under the spring is frictionless. A block of mass 1.00 kg is released from rest at A. After sliding on the track, it compresses the spring by 0.220 m before rebounding. Calculate the following:
(a) The velocity of the block at point B.
(b) the thermal energy produced as the block slides from B to C;
(c) the velocity of the block at point C;
(d) the stiffness constant k for the spring.

Explanation / Answer

a) 0.5*m*VB^2 = m*g*h

==> VB = sqrt(2*g*h)

= sqrt(2*9.8*2)

= 6.26 m/s

b) workdone by friction = thermal enrgy produced

= mue_k*m*g*BC

= 0.25*1*9.8*3.5

= 8.575 J

c) a = -mue*g = -0.25*9.8 = -2.45 m/s^2

VC^2 - VB^2 = 2*a*BC

VC = sqrt(VB^2 + 2*a*BC)

= sqrt(6.26^2 - 2*2.45*3.5)

= 4.694 m/s

d) 0.5*k*x^2 = 0.5*m*VC^2

k = m*VC^2/x^2

= 1*4.694^2/0.22^2

= 455.24 N/m

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