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 ▸How can a car be changing velocity yet not changing speed?
A projectile is launched from ground level with a speed of 25 m/s at an angle of 42° to the horizontal. What is the horizontal distance from the starting point of the projectile when it hits the ground?
An infared wave has a wavelength of 1.5 x10^–6 m. The speed of this wave is 2.2 × 10^8 m/s. Calculate the frequency of the wave. Give your answer in standard form and to 2 significant figures.
State what is meant by a Doppler shift and describe how it was used to study the movement of galaxies.