Acar of mass m accelerates from speed v1 to speed v2 while going up a slope that makes an angle θ with the horizontal. the coefficient of static friction is μs, and the acceleration due to gravity is g. find the total work w done on the car by the external forces. express your answer in terms of the given quantities. you may or may not use all of them.

In the derivation of rrkm theory, a factor of 1/2 is introduced when equalizing the rates of formation and decomposition of activated complex as keal-hr) = ko this is clearly against the assumption of transition state theory that states all the activated complex in the transition state iss going to the product. find the reason why this factor is introduced here.

In a thunderstorm, charge builds up on the water droplets or ice crystals in a cloud. thus, the charge can be considered to be distributed uniformly throughout the cloud. for the purposes of this problem, take the cloud to be a sphere of diameter 1.00 kilometer. the point of this problem is to estimate the maximum amount of charge that this cloud can contain, assuming that the charge builds up until the electric field at the surface of the cloud reaches the value at which the surrounding air breaks down. this breakdown means that the air becomes highly ionized, enabling it to conduct the charge from the cloud to the ground or another nearby cloud. the ionized air will then emit light due to the recombination of the electrons and atoms to form excited molecules that radiate light. in addition, the large current will heat up the air, resulting in its rapid expansion. these two phenomena account for the appearance of lightning and the sound of thunder. take the breakdown electric field of air to be eb=3.00ă—106n/c. part a estimate the total charge q on the cloud when the breakdown of the surrounding air is reached. express your answer numerically, to three significant figures, using ďµ0=8.85ă—10â’12c2/(nâ‹…m2) .

Determine the maximum r-value of the polar equation r =3+3 cos 0