Problem

The car A has a weight of 4500 lb and is traveling to the right at 3 ft/s. Meanwhile a 300...

The car A has a weight of 4500 lb and is traveling to the right at 3 ft/s. Meanwhile a 3000-lb car B is traveling at 6 ft/s to the left. If the cars crash head-on and become entangled, determine their common velocity just after the collision. Assume that the brakes are not applied during collision.

Step-by-Step Solution

Solution 1

Weight of a car \(A\left(W_{A}\right)=4500 \mathrm{lb}\)

Velocity of a car \(A\left(v_{A}\right)=3 \mathrm{ft} / \mathrm{s}\)

Weight of a car \(B\left(W_{B}\right)=3000 \mathrm{lb}\)

Velocity of a car \(B\left(v_{B}\right)=6 \mathrm{ft} / \mathrm{s}\)

Fred body diagram

Conservation of linear momentum

$$ \begin{aligned} &(+) m_{A}\left(v_{A}\right)_{1}+m_{B}\left(v_{B}\right)_{1}=\left(m_{A}+m_{B}\right) v_{2} \\ &\frac{W_{A}}{g}\left(v_{A}\right)_{1}-\frac{W_{B}}{g}\left(v_{B}\right)_{1}=\left(\frac{W_{A}}{g}+\frac{W_{B}}{g}\right) v_{2} \\ &v_{2}=\frac{4500 \times 3-3000 \times 6}{4500+3000} \\ &v_{2}=-0.6 \mathrm{~m} / \mathrm{s} \end{aligned} $$

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