The figure below shows the potential energy function U (r)for a particle moving

Question

The figure below shows the potential energy function U (r)for a particle moving along an axis labeled by the coordinate r. Values for energy and distance are in joules (j) millimeters (mm), respectively. The total energy of this particle is E = -4 J. Initially, the particle is at r = 1 mm and moving to the right (direction of increasing r) Which of the following statements best describes the subsequent motion of this particle? a. The particle continues moving rightward, with no apparent limit. b The continues moving rightward until it reaches the equilibrium point at c The continues moving rightward until it reach the turning point at r 2.2 mm, after which no further motion occurs. d The motion of the particle continues indefinitely, but is confined to the range of coordinates bounded by the turning point at r 0.8 mm and r 2.2 mm. e. The motion of the particle continues indefinitely, but is confined to the range of coordinates bounded by the turning point at r 0.8 mm and r 3.3 mm. A 0.20 kg object attached to the end of a string swings in a vertical of radius 0.80 m. At the top of the circle the speed of the object is 4.5 m/s. What is the tension in the string at this position? a. 2.0 N b. 3.1 N c. 3.2 N d. 5.1 N e. 7.0 N

Explanation / Answer

Turning points are the points where the total energy is equal to the potential energy only and kinetic energy is zero.

a The particle continued moving rightwards with no apparent limit.

When the object is at the top tension, normal force and weight act vertically downwards.

T + mg = mv^2 / R

T = m ( v^2 / R - g) = 0.2 ( 4.5^2/0.8 - 9.8)

= 3.1 N

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