3. Consider a car that weighs about 2000 kg (4400 lb) and is parked at an elevat

ID: 1650433 • Letter: 3

Question

3. Consider a car that weighs about 2000 kg

(4400 lb) and is parked at an elevation of

30m (100 ft) above the bottom of a hill with a

constant slope equal to 0.5. [Recall that the

acceleration of gravity is g 9.8 m/s2.]

(a) What is the force on the car along the slope

of the hill (in SI units)?

(b) Estimate the final kinetic energy the car

would have if its brakes gave way and it

freely rolled down to the bottom of the hill

(in SI units).

car in both m/s and mph units.

(A) slope = tan(theta) = 0.5

theta = tan^-1(0.5)

= 26.6 deg

along the incline, F = m g sin(theta)

F = (2000 x 9.81 ) sin26.6 Or 4400 sin(26.6)

F = 8785 N or 1970 lb ...........Ans

(B) deltaH = 30 m

KE = m g deltaH

= 2000 x 9.8 x 30

= 588000 J

588000 = 2000 v^2 / 2

v = 24.25 m/s Or 54.25 mph

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