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36-40
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Question 36 The particle of mass m and angular momentum I such that L² = 10m Vo R² moves in a potential 3.R V(7) = -Vo + Vo > 0. 7' The radius of the stable circular orbit is 3R 4R R 2R Question 37 1 pts The force of interaction between a particle of mass m₁ and a second particle of mass m₂ separated by a distance r is given by an attractive gravitational and a repulsive force that is proportional to r with probability constant C, Gm1m₂ с F(r) + p² gu3 Find the stable equilibrium position ro. ro = 0 To = C(m₁+m₂) Gm² m²/ TO C(m₁+m₂) ² Gm1m₂ To = C Gm1m₂ Question 38 1 pts The force of interaction between a particle of mass m₁ and a second particle of mass m₂ separated by a distance r is given by an attractive gravitational force and a repulsive force that is proportional to r probability constant C, with F(r) Gm1m₂ C + p2 p3 Find the angular frequency of small oscillation about the stable equilibrium position. 3 C m1m₂ (m₁ + m₂) 3 G4 m1m₂ (m₁ + m₂) 3 G₁ (mm²) * (m₁-m₂) M1M2 3 G4 mi+m₂ C M1M2 1 pts

Question 39 1 pts A disk of mass m and radius R is attached to a spring of constant Kas shown in the figure. The disk rolls and forth without slipping. The angular frequency of the motion of the disk is ak 3m K vooooo R What is the value of a? 1 2 3/2 1/2 2/3 Question 40 1 pts Consider replacing the pair of polar coordinates r and by the pair of coordinates r and q where q sin . What is the kinetic energy of a = particle? Om (r²q² + ²q²) ○ 1/2m (r² + r²ġ²) m 01/11 (² (r² + r² ġ²) 2 1-q² ○ 1⁄m (r² + r² 0² ġ²) O / m (r² + 1 + ²2 )