Question

(a) How high a hill can a car coast up (engine disengaged) if friction is negligible and its initial speed is 106 km/h? 44.18 Correct: Your answer is correct. m

(b) If, in actuality, a 750 kg car with an initial speed of 106 km/h is observed to coast up a hill to a height 20.0 m above its starting point, how much thermal energy was generated by friction? 177.87 Incorrect: Your answer is incorrect. J

(c) What is the average force of friction if the hill has a slope 2.5° above the horizontal? 5322.26 Incorrect: Your answer is incorrect. N (down the slope)

(c)

Find the useful power output (in W) of an elevator motor that lifts a 2500 kg load a height of 30.0 m in 12.0 s, if it also increases the speed from rest to 4.00 m/s. Note that the total mass of the counterbalanced system is 10,000 kg—so that only 2500 kg is raised in height, but the full 10,000 kg is accelerated.

W

(d)

What does it cost (in cents), if electricity is $0.0900 per kW · h?

cents

Answer #1

(b) Mass of the car m = 750 kg

initial speed u = 106 km/h

= 106 (1000 m/3600 s)

= 29.444 m/s

height h = 20.0 m

Initial Kinetic energy of the car K = (1/2) mv ^{2}

K = (1/2)(750)(29.444) ^{2}

= 325115.75 J

Potential energy of the car at the top P = mgh

P = (750)(9.8)(20)

= 147000 J

Thermal energy was generated by frictionQ = K -E S i nce from law of conservation of energy

Q =(325115.75) -147000

= 178115.75 J

(c) the average force of friction if the hill has a slope 2.5° above the horizontal f = ?

We know Q = f S

Where S = length along the incline = h / sin 2.5
^{o}

= 20 m/0.0436

= 458.51 m

So,f = Q / S

= (178115.75) /458.51

= 388.46 m

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