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 2.1 m long with a coefficient of kinetic friction ?k = 0.22. 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 0.25 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.

vB = ?

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.

E = ?

Part C

Determine the velocity of the block at point C.

Express your answer to two significant figures and include the appropriate units.

vC = ?

Part D

Determine the stiffness constant k for the spring.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

part A:

from the law of conservation of energy

0.5 mVb^2 = mg r

Vb^2 = 2 g r

Vb^2 = 2 * 9.81 * 2

Vb = 6.3 m/s

0--------------------------------------

part B:

Energy produced thermal = u m g d

E = 0.2* 1 * 9.8* 2.1 /1)

E =

E = 4.116 Joules

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part C:

From Energy COnservation

0.5 mVb^2 = 0.5 mVc^2 + Ek

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

Vc^2 = (6.26^2 - (2* 4.11)/1

Vc = 5.567 m/s

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[part D:

EPE = KE

0.5 kx^2 = 0.5 mVc^2

K = 1 * 5.567^2/(0.25^2)

K = 495.86 N/m

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