Using the work-energy theorem to investigate a traffic scene A car hit a pedestrian and immediately the driver slammed on the brakes to stop the car. During the subsequent trial, the driver's lawyer claimed his client was obeying the posted 35-mi/hr speed limit. You have been called in as the state's expert witness. Your investigation of the accident found that the skid marks made while the brakes were applied until the car stopped were Ax = 94 m long. You also measured the coefficient of kinetic friction between the car's tires and the road (using a drag sled) to be μk = 0.36. (a) Use the work-energy theorem to show that the car's minimum speed vo when the driver slammed on the brakes is given by vo = √2 μg Ax (b) Use the result of part (a) to determine if the car was speeding when the pedestrian was hit. [answer: The car's speed was at least 57 mi/hr when the brakes were applied.] (c) If the car's mass is 1470 kg, how much heat energy was produced while the car was skidding? [answer: 4.9 x 10³ JJ W = AK Q=- AK g=9.81 m/s² K = 1/2mv² fk = UkN 1.0 mi/hr = 0.45 m/s W = (Fcose)Ax w = mg

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**Using the work-energy theorem to investigate a traffic scene**

A car hit a pedestrian and immediately the driver slammed on the brakes to stop the car. During the subsequent trial, the driver’s lawyer claimed his client was obeying the posted 35-mi/hr speed limit. You have been called in as the state's expert witness. Your investigation of the accident found that the skid marks made while the brakes were applied until the car stopped were Δx = 94 m long. You also measured the coefficient of kinetic friction between the car’s tires and the road (using a drag sled) to be μₖ = 0.36.

(a) Use the work-energy theorem to show that the car's minimum speed v₀ when the driver slammed on the brakes is given by \( v_0 = \sqrt{2 \, \mu_k \, g \, \Delta x}. \)

(b) Use the result of part (a) to determine if the car was speeding when the pedestrian was hit. [answer: The car's speed was at least 57 mi/hr when the brakes were applied.]
  
(c) If the car's mass is 1470 kg, how much heat energy was produced while the car was skidding? [answer: 4.9 x 10⁵ J]

\[ W = \Delta K \]

\[ Q = -\Delta K \]

\[ g = 9.81 \, \text{m/s}^2 \]

\[ 1.0 \, \text{mi/hr} = 0.45 \, \text{m/s} \]

\[ K = \frac{1}{2} \, m v^2 \]

\[ W = (F \cos \theta) \Delta x \]

\[ f_k = \mu_k N \]

\[ w = mg \]
Transcribed Image Text:**Using the work-energy theorem to investigate a traffic scene** A car hit a pedestrian and immediately the driver slammed on the brakes to stop the car. During the subsequent trial, the driver’s lawyer claimed his client was obeying the posted 35-mi/hr speed limit. You have been called in as the state's expert witness. Your investigation of the accident found that the skid marks made while the brakes were applied until the car stopped were Δx = 94 m long. You also measured the coefficient of kinetic friction between the car’s tires and the road (using a drag sled) to be μₖ = 0.36. (a) Use the work-energy theorem to show that the car's minimum speed v₀ when the driver slammed on the brakes is given by \( v_0 = \sqrt{2 \, \mu_k \, g \, \Delta x}. \) (b) Use the result of part (a) to determine if the car was speeding when the pedestrian was hit. [answer: The car's speed was at least 57 mi/hr when the brakes were applied.] (c) If the car's mass is 1470 kg, how much heat energy was produced while the car was skidding? [answer: 4.9 x 10⁵ J] \[ W = \Delta K \] \[ Q = -\Delta K \] \[ g = 9.81 \, \text{m/s}^2 \] \[ 1.0 \, \text{mi/hr} = 0.45 \, \text{m/s} \] \[ K = \frac{1}{2} \, m v^2 \] \[ W = (F \cos \theta) \Delta x \] \[ f_k = \mu_k N \] \[ w = mg \]
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