Car Crash Scenario?
A car is traveling at a constant speed of 20 m/s when the driver suddenly applies the brakes to avoid hitting a child standing on the road. Meanwhile, a tree is approaching the car at a speed of 5 m/s. What is the minimum coefficient of friction required between the car's tires and the road to prevent the car from hitting the tree?
1 Answer
📌 CONCEPT: The car must have enough frictional force to prevent it from hitting the tree, given the relative motion between the car and the tree.
📐 RULE / FORMULA: According to Newton's second law of motion, the maximum possible deceleration of the car is given by a = μg, where μ is the coefficient of friction and g is the acceleration due to gravity.
💡 WORKED EXAMPLE: Given the initial speed of the car (v = 20 m/s), the speed of the tree (v_tree = 5 m/s), and the deceleration (a), we can find the minimum coefficient of friction required using the equation v^2 = u^2 + 2as, where v is the final velocity (0 m/s), u is the initial velocity (20 m/s), a is the deceleration, and s is the distance (which we don't need to find). Then we can use the formula a = μg to find μ.
⚠️ COMMON MISTAKE: Students often forget to consider the relative motion between the car and the tree, or they incorrectly assume that the car's deceleration is independent of the tree's motion.
01 Nov 26
🔗 More from Chapter 4: Laws of Motion
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