Problem 8.36 Constantsl c Table Part A Consider the track shown in the figure. T

Question

Problem 8.36 Constantsl c Table Part A 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 4.0 m long with a coefficient of kinetic friction ?k-0.19. 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) Determine the velocity of the block at point B Express your answer to two significant figures and include the appropriate units Value Units Submit Request Answer Part B Figure 1 of 1 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 m 1.0 kg r 2.0 m B-1 Value Units

Explanation / Answer

a)

Initially the block is at a heigth of r = 2 m above the ground at point A when it start's sliding from point A velocity of block at point B is

VB = sqrt(2g*r)

VB = sqrt(2 x 9.81 m/s^2 x 2 m)

VB = 6.26 m/s

b)

Energy lost as is moves from point B to C

Ek = uk*m*g*d

Ek = 0.19 x 1 kg x 9.81 m/s^2 x 4 m

Ek = 7.46 J

c)

According to the law of conservation of energy

1/2m*VB^2 = 1/2mVc^2 + Ek

1/2mVc^2 = 1/2m*VB^2 - Ek

Vc^2 = VB^2 - 2Ek / m

Vc = sqrt(VB^2 - 2Ek / m)

Vc = sqrt(6.26^2 - 2*7.46/1)

Vc = 4.93 m/s

d)

from conservation of energy

1/2mVc^2 = 1/2kx^2

k = mVc^2 / x^2

k = (1 x 4.93^2) / (0.20)^2

k = 607.6 N/m

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