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Answer :
Potential Energy of the car at the top of the hill: The car has Potential energy when it is raised to a certain height against the gravitational force. The potential energy is a product of mass (m), gravity (g), and height (h). Therefore the Potential energy of the car at the top of the hill is calculated as follows: P.E= mgh where m = 750 kg g = 9.8 m/s²h = 15 mP. E= 750 kg * 9.8 m/s² * 15 m = 110250 J Potential Energy of the car at the top of the hill = 1.1025 × 10⁵ J.
The work done by friction is calculated using the following formula: Work = Force x distance The distance traveled by the car (s) = 125m - 0m = 125mThe initial velocity of the car, u = 0The final velocity of the car, v = 35 km/h = 9.72 m/sThe average velocity of the car, v = (u + v) / 2 = (0 + 9.72) / 2 = 4.86 m/s Therefore the Work done by friction on the car is calculated as follows: W = Fd = 0.5 * 750 * (55/3.6)² - 0.5 * 750 * (35/3.6)²W = 118356 J - 57656 J Work done by friction = 60.7 kJ.
From the conservation of energy principle, the Potential Energy of the car at the top of the hill is equal to the kinetic energy of the car at the bottom of the hill when friction is neglected. i.e P.E = K.E = 0.5 * m * v²Therefore, the kinetic energy of the car at the bottom of the hill is given as: K.E = 0.5 * m * v²where m = 750 kgv = 55 km/h = 15.27 m/sK.E = 0.5 * 750 * (15.27)² = 840406 J Now the work done by friction on the car is calculated as follows: Work done by friction (W) = K.E - P.E = 840406 J - 1.1025 × 10⁵ J = 730156 J
The force of friction acting on the car is given by the formula: F = W / d where W is the work done by friction and d is the distance traveled by the car F = W / d = 730156 J / 125 mF = 5841 N Therefore, the force of friction acting on the car is 5841 N.
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