Suppose a car approaches a hill and has an initial speed of 106 km/h at the bott

Question

Suppose a car approaches a hill and has an initial speed of 106 km/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. B. If in actuality a 780 kg car with an initial speed of 106 km/h is observed to coast up a hill and stops at a height 21.5m above its starting point, how much thermal energy was generated by friction in J? C. What is the magnitude of the average force in Newtons of friction if the hill has a slope of 27 deg. above the horizontal.

Explanation / Answer

mass of the car, m=780 kg

car initial speed, v=106 km/h

height, h=21.5m

theta=27 degrees

a)

K.E=1/2*m*v^2

=1/2*780*(106*1000/(60*60))^2

=3.38*10^5 J

and

P.E=m*g*h

=780*9.8*21.5

=1.643*10^5 J

now,

thermal energy due to friction, Q=K.E-P.E

Q=1.74*10^5 J

b)

work done=1.74*10^5

F*d=1.74*10^5

F*(h/sin(theta))=1.74*10^5

F*(20.5/sin(27))=1.74*10^5

===> F=3853.4 N

force F=3.85*10^3 N

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