A car of mass M and a maximum power output of P is on an rough inclined plane Θ to the horizontal. What is the maximum velocity (v). Coefficient of friction=μ and air resistance=kv where k is constant
At the maximum velocity the driving force of the car is equal to the sum of the opposing forces: Fdriving=Ffriction+Fair+mgsinΘ Ffriction=mgμcosΘ Fair=kv p=[mgμcosΘ+ kv+mgsinΘ]v = [μcosΘ+sinΘ]mgv+kv2 kv2+[μcosΘ+sinΘ]mgv-p=0 solve using the quadratic equation: v= -[μcosΘ+sinΘ]mg ± [ ([μcosΘ+sinΘ]mg)2+4kp]1/2 . 2k We only want the positive root as, the direction of velocity is up the incline therefore: v= -[μcosΘ+sinΘ]mg + [ ([μcosΘ+sinΘ]mg)2+4kp]1/2 . 2k
JB
Related Physics A Level answers
All answers ▸The speed of water moving through a turbine is 2.5 m/s. Show that the mass of water passing through an area of 500 metres squared in one second is about 1 x 10^6 kg (density of sea water = 1030 kg/m^3)
How many joules of heat energy are required to raise the temperature of 10kg of water from 22⁰C to 27⁰C? (The Specific Heat Capacity of water is 4200 Jkg^-1⁰C^-1)
A cylindrical specimen of material with diameter 1.5x10^-4 has a breaking stress of 1.3GPa. Calculate the tensile force acting on the specimen at breaking point.
A light wave has a wavelength of 420nm, calculate the energy of this wave in joules.