Question

A Porsche 944 Turbo has a rated engine power of 217hp . 30% of the power is lost in the drive train, and 70% reaches the wheels. The total mass of the car and driver is 1520 kg, and two-thirds of the weight is over the drive wheels.
a) What is the maximum acceleration of the Porsche on a concrete surface where μs=1?

b) What is the speed of the Porsche at maximum power output?

c) If the Porsche accelerates at amax , how long does it take until it reaches the maximum power output?

Answer 1

Explanation:

(a)  It is given that two-third of weight is over the drive wheels. So, mathematically, w = $\frac{2}{3}mg$.

Hence, maximum force is expressed as follows.

                $F_{max} = \mu_{s} \times w$

           $m \times a_{max} = \mu_{s} (\frac{2}{3} mg)$

Hence, the maximum acceleration is calculated as follows.

             $a_{max} = \frac{2}{3} \mu_{s} \times g$

                          = $\frac{2}{3} \times 1.00 \times 9.8 m/s^{2}$

                          = 6.53 $m/s^{2}$

Hence, the maximum acceleration of the Porsche on a concrete surface where μs = 1 is 6.53 $m/s^{2}$.

(b)  Since, 30% of the power is lost in the drive train. So, the new power is 70% of $P_{max}$.

That is,   new power = $0.7 \times P_{max}$

Now, the expression for power in terms of force and velocity is as follows.

                      P = $F_{max} \nu$

              $0.7 P_{max} = ma_{max} \nu$

Therefore, speed of the Porsche at maximum power output is as follows.

            $\nu = 0.7 \times \frac{P_{max}}{ma_{max}}$

                      = $0.7 \times \frac{217 hp \times \frac{746 W}{1 hp}}{1500 kg \times 6.53 m/s^{2}}$

                      = 11.568 m/s

                      = 11.57 m/s

Therefore, speed of the Porsche at maximum power output is 11.57 m/s.

(c)   The time taken will be calculated as follows.

             time = $\frac{\text{velocity}}{\text{acceleration}}$

                     = $\frac{11.57 m/s}{6.53 m/s^{2}}$

                     = 1.77 s

Therefore, the Porsche takes 1.77 sec until it reaches the maximum power output.