You set off on your journey without checking your gas tank. The “low fuel” light

Question

You set off on your journey without checking your gas tank. The “low fuel” light comes on just as the engine stalls as you keep rolling. You see a gas station at the top of a 30 meter high hill. Before you start up the hill, your speedometer reads 25 m/s (yes, you retrotted your car with a physics appropriate speedometer). You settle into the seat and hope for the best. As you crest the hill and pull into the gas station you coast to a standstill. Looking back, you notice a sign that says “Caution: 10% grade .” To pass the time while the attendant lls your tank, use work and energy to compute the coefcient of rolling friction for your car.

Explanation / Answer

given data

initial speed of the car, u = 25 m/s

final speed, v = 0

h = 30 m

angle of inclination, theta = tan^-1(0.1)

= 5.7 degrees

distance travelled by the car, d = h/sin(5.7)

= 30/sin(5.7)

= 301.5 m

net workdone = change in kinetic energy

W_friction + W_gravity = 0.5*m*(v^2 - u^2)

-mue_k*m*g*d - m*g*h = 0.5*m*(0^2 - u^2)

mue_k*m*g*d + m*g*h = 0.5*m*u^2

mue_k*g*d + g*h = 0.5*u^2

mue_k*g*d = 0.5*u^2 - g*h

mue_k = 0.5*u^2/(g*d) - g*h/(g*d)

mue_k = 0.5*25^2/(9.8*301.5) - 30/(301.5)

= 0.00626

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