We live on our mild climate in oblivious serenity with our nearly circular stable orbit while in another universe, the force of gravity is instead F(r) = −k/r3 . Calculate the effective potential energy and characterize stability for possible orbits with a variety of energy & angular momentum initial conditions (ie pφ less than, equal to, and greater than µk). Calculate the orbit shapes for each of these conditions.

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?

Ryan is examining the energy of the particles in a bar of gold. what is ryan most likely studying?

The temperature in gavin's oven is a sinusoidal function of time. gavin sets his oven so that it has a maximum temperature of 280°f and a minimum temperature of 240°. once the temperature hits 280°, it takes 20 minutes before it is 280° again. gavin's cake needs to be in the oven for 30 minutes at temperatures at or above 270°. he puts the cake into the oven when it is at 260° and rising. how long will gavin need to leave the cake in the oven? (round your answer to the nearest minute.)