Suppose a car approaches a hill and has an initial speed of 116 km/h at the bottom of the hill. The driver takes her foot off of the gas pedal and allows the car to coast up the hill.
Randomized Variablesvi = 116 km/h
m = 780 kg
h = 20.5 m
a = 2.3 °
Part (a) If the car has the initial speed stated at a height of h = 0, how high (in m) can the car coast up a hill if work done by friction is negligible?
Part (b) If, in actuality, a 780-kg car with an initial speed of 116 km/h is observed to coast up a hill and stops at a height 20.5 m above its starting point, how much thermal energy was generated by friction in J?
U2 + K2 = U1 + K1 + W_other
U2 is final potential energy.
K2 is final kinetic energy.
The Attempt at a Solution
Part (a) I got right.
1/2(mv^2) + mgh = 0
h = v^2/(2g)
=(32.2 m/s)^2 /(2*9.8m/s^2) = 52.9m
Part (b) I need help. (FK stands for friction force and s stands for displacement.)
I tried U2 + 0 = U1 + K1 + W_other.
W_other = -FK*s = U2 - U1 - K1
-FK*s = mg(Y2 - Y1) - 1/2(m*v^2)
-FK*s = 780kg*9.8m/s^2(20.5m*sin(2.3) - 52.9m) - 1/2(780kg*(32.2m/s)^2)
-FK*s = -652033j
FK = -(-652033j) / s
FK = 652033 j / (20.5m - 52.9m)
FK = -20124 N
The correct answer is 248200 j