Problem number 3 (10pts) a particle of mass m is constrained to move on the parabola z=-in the plane, a is a constant length, and there is a constant gravitational force acting in the negative z direction. (a) [3 points] write the lagrangian using as the generalized coordinate of the particle. (b) [2 points] write the equation of motion from the lagrangian? (c) [3 points] write the equation for small oscillations about the equilibrium point. (d) [2 points] what is the angular frequency for the small oscillations in (c)?

Balloon a has charge q, and identical mass balloon b has charge 10q. you hang them from threads near each other. choose all of the statements with which you agree. check all that apply. a. a and b exert the same magnitude forces on each other. b. the force that a exerts on b is 10 times the force that b exerts on a. c. the angle between the thread supporting a and the vertical is < the angle between the thread supporting b and the vertical. d. the force that a exerts on b is 1/10 the force that b exerts on a.

While you are driving in the lane next to the curb on a multi-lane road the car on your left suddenly moves toward you lane. they are about toy crash into your front fender. you

Adiver named jacques observes a bubble of air rising from the bottom of a lake (where the absolute pressure is 3.50 atm) to the surface (where the pressure is 1.00 atm). the temperature at the bottom is 4.00 ∘c, and the temperature at the surface is 23.0 ∘c.what is the ratio of the volume of the bubble as it reaches the surface (vs) to its volume at the bottom (vb)? if jaques were to hold his breath the air in his lungs would be kept at a constant temperature. would it be safe for jacques to hold his breath while ascending from the bottom of the lake to the surface?