Respuesta :
Explanation:
(a) It is given that two-third of weight is over the drive wheels. So, mathematically, w = [tex]\frac{2}{3}mg[/tex].
Hence, maximum force is expressed as follows.
[tex]F_{max} = \mu_{s} \times w[/tex]
[tex]m \times a_{max} = \mu_{s} (\frac{2}{3} mg)[/tex]
Hence, the maximum acceleration is calculated as follows.
[tex]a_{max} = \frac{2}{3} \mu_{s} \times g[/tex]
= [tex]\frac{2}{3} \times 1.00 \times 9.8 m/s^{2}[/tex]
= 6.53 [tex]m/s^{2}[/tex]
Hence, the maximum acceleration of the Porsche on a concrete surface where μs = 1 is 6.53 [tex]m/s^{2}[/tex].
(b) Since, 30% of the power is lost in the drive train. So, the new power is 70% of [tex]P_{max}[/tex].
That is, new power = [tex]0.7 \times P_{max}[/tex]
Now, the expression for power in terms of force and velocity is as follows.
P = [tex]F_{max} \nu[/tex]
[tex]0.7 P_{max} = ma_{max} \nu[/tex]
Therefore, speed of the Porsche at maximum power output is as follows.
[tex]\nu = 0.7 \times \frac{P_{max}}{ma_{max}}[/tex]
= [tex]0.7 \times \frac{217 hp \times \frac{746 W}{1 hp}}{1500 kg \times 6.53 m/s^{2}}[/tex]
= 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 = [tex]\frac{\text{velocity}}{\text{acceleration}}[/tex]
= [tex]\frac{11.57 m/s}{6.53 m/s^{2}}[/tex]
= 1.77 s
Therefore, the Porsche takes 1.77 sec until it reaches the maximum power output.
