College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Question
#5
![**Conceptual Question:**
Someone claims that a car doubling its speed (say from 30 mph to 60 mph) that crashes into a wall will be "twice" as damaging. Do you agree? Explain.
**Analysis:**
When considering the damage caused by a car crash, it's important to look at the kinetic energy involved. The kinetic energy (KE) of an object is given by the formula:
\[ \text{KE} = \frac{1}{2}mv^2 \]
where \( m \) is the mass of the object and \( v \) is its velocity.
In this scenario, if the car's speed doubles from 30 mph to 60 mph, the velocity component in the kinetic energy equation (which is squared) will result in the kinetic energy becoming four times greater. Hence, the damage potential increases with the square of the speed, not just linearly.
Therefore, doubling the speed of the car results in kinetic energy—and consequently the potential for damage—that is four times greater, not merely twice as damaging. Hence, the statement that it would be "twice" as damaging is incorrect.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1af144b1-86f1-4bbf-876f-693f648ad264%2F430fa452-1f74-4ddb-b14b-fbfc1834fac0%2Fqpqmh0i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Conceptual Question:**
Someone claims that a car doubling its speed (say from 30 mph to 60 mph) that crashes into a wall will be "twice" as damaging. Do you agree? Explain.
**Analysis:**
When considering the damage caused by a car crash, it's important to look at the kinetic energy involved. The kinetic energy (KE) of an object is given by the formula:
\[ \text{KE} = \frac{1}{2}mv^2 \]
where \( m \) is the mass of the object and \( v \) is its velocity.
In this scenario, if the car's speed doubles from 30 mph to 60 mph, the velocity component in the kinetic energy equation (which is squared) will result in the kinetic energy becoming four times greater. Hence, the damage potential increases with the square of the speed, not just linearly.
Therefore, doubling the speed of the car results in kinetic energy—and consequently the potential for damage—that is four times greater, not merely twice as damaging. Hence, the statement that it would be "twice" as damaging is incorrect.
Expert Solution
Step 1
Given:-
The speed of the car vi = 30 mph = 13.412 m/s
The speed of the car vf = 60 mph = 26.82 m/s
Find:-
Crashes into a wall will be "twice" as damaging when the speed gets double? explain
Step by step
Solved in 3 steps
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