At night while it is dark, a driver inadvertently parks his car on a drawbridge.

Question

At night while it is dark, a driver inadvertently parks his car on a drawbridge. Some time later, the bridge must be raised to allow a boat to pass through. The coefficients of friction between the bridge and the car's tires are mu_s = 0.820 and mu_k = 0.450. Start each part of your solution to this problem with a free-body diagram of the car. A) At what angle will the car just start to slide? B) If the bridge attendant sees the car suddenly start to slide and immediately turns off the bridge's motor, what will be the car's acceleration after it has begun to move?

Explanation / Answer

car will slide when the weight component of the car exceeds the friction force
mgsinx >mgcosx

==> < gtanx

x= tan-1(/g)n =tan-1(0.82/9.8 )= angle = 4.78 degrees. ( in rest use , static friction co eff)

the cars acceleration = g = 0.45 X 9.8= 4.41m/s^2 ( in motion use kinetic friction co eff)

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