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)?

How many molecules are present in 3 mols of silicon dioxide (sio2)?

You are a sales representative for a company that makes a new alternate fuel for vehicles. you have prepared a presentation for the environmental engineers to sell your new product. what question do you expect the audience to ask regarding whether the new fuel will cause less damage to the environment? a. do we have to change any parts of the vehicle to use this alternate fuel? b. will the vehicles get better fuel mileage with the alternate fuel? c. how much greenhouse gas does your fuel produce compared with current fuel sources? d. is the alternate fuel more expensive than fossil fuel?

What property of an object determines its inertia?