Suppose a car approaches a hill and has an initial speed of

106

k

m

/

h

at the bottom of the hill. The driver takes her foot off the gas pedal and allows the car to coast up the hill.

A. If in actuality a

780

k

g

car with an initial speed of

106

k

m

/

h

is observed to coast up a hill and stops at a height

21.5

m

above its starting point, how much thermal energy was generated by friction in

J

?

B. What is the magnitude of the average force in newtons of friction if the hill has a slope of

27

∘

above the horizontal.

a) 1.73*10^5 J

b) 3645 N

Explanation:

106 km/h = 106 * 1000/3600 = 29.4 m/s

If KE = PE, then

mgh = 1/2mv²

gh = 1/2v²

h = v²/2g

h = 29.4² / 2 * 9.81

h = 864.36 / 19.62

h = 44.06 m

Loss of energy = mgΔh

E = 780 * 9.81 * (44.06 - 21.5)

E = 7651.8 * 22.56

E = 172624.6 J

Thus, the amount if energy lost is 1.73*10^5 J

Work done = Force * distance

Force = work done / distance

Force = 172624.6 / (21.5/sin27°)

Force = 172624.6 / 47.36

Force = 3645 N

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reserve is the answer