A 1.0-kg object is moving without friction along the x-axis. The potential energ

Question

A 1.0-kg object is moving without friction along the x-axis. The potential energy curve as a function of position is shown in the figure, and the system is conservative. The speed of the object at position x=2.0 m is 2.0 m/s. a) What is the total mechanical energy of the object? Explain how you found it. b) What will be its speed at 7.0 m along the +x-axis? c) Are there turning points? Where are the turning points, at what positions? d) Identify the regions in which the force points in the positive x-axis direction. Explain your answer.

Explanation / Answer

a)

at x = 2 m :

U = potential energy = 6 J

v = speed = 2 m/s

m = mass = 1 kg

kinetic energy is given as

KE = (0.5) m v2 = (0.5) (1) (2)2 = 2 J

Total mechanical energy is given as

E = KE + U = 2 + 6 = 8 J

b)

at x = 7 m :

U = potential energy = 7 J

Total mechanical energy remain same at all points

E = total mechanical energy = 8 J

hence

E = U + KE

8 = 7 + KE

KE = 1

(0.5) m v2 = 1

(0.5) (1) v2 = 1

v = 1.41 m/s

c)

turning points are the points where KE = 0

hence E = mechanical energy = U

U = potential energy = 8 J

from the graph , U = 8 J at

x = 0.5 m

and x = 8 m

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