/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 85 You are in charge of an accident... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 85

You are in charge of an accident reconstruction case for the local police department. In order to determine car speeds, skid mark lengths are measured. To determine the coefficient of kinetic friction, you get into an identical car, and at a speed of \(65.2 \mathrm{mi} / \mathrm{h}\), you lock its brakes and skid \(51.5 \mathrm{~m}\) to rest. (a) Determine the car's deceleration. (b) What is the coefficient of kinetic friction between the tires and road surface? (c) The car in the accident actually skidded \(57.3 \mathrm{~m}\). What was its initial speed?

Short Answer

Expert verified
(a) Deceleration is \(-8.25 \text{ m/s}^2\). (b) Coefficient of friction is \(0.84\). (c) Initial speed was \(68.8 \text{ mi/h}\).

Step by step solution

01

Convert Speed to Meters Per Second

First, convert the car's initial speed from miles per hour to meters per second. We use the conversion: \(1 \text{ mile} = 1609.34 \text{ meters}\) and \(1 \text{ hour} = 3600 \text{ seconds}\). Thus, \(65.2 \text{ mi/h} = 65.2 \times \frac{1609.34}{3600} \text{ m/s} = 29.14 \text{ m/s}\).
02

Determine the Car's Deceleration

Using the kinematic equation \(v^2 = u^2 + 2a s\), where \(v = 0\) (final velocity), \(u = 29.14 \text{ m/s}\) (initial velocity), \(s = 51.5 \text{ m}\) (distance), solve for \(a\) (deceleration): \[0 = (29.14)^2 + 2a(51.5)\] \[a = -\frac{(29.14)^2}{2 \times 51.5} \approx -8.25 \text{ m/s}^2\]
03

Calculate Coefficient of Kinetic Friction

Use the formula for deceleration due to friction: \(a = \mu g\), where \(\mu\) is the coefficient of kinetic friction and \(g = 9.81 \text{ m/s}^2\) (acceleration due to gravity). Solve for \(\mu\):\[\mu = \frac{a}{g} = \frac{-8.25}{9.81} \approx 0.84\]
04

Determine Initial Speed of Accident Car

Using the same kinematic formula \(v^2 = u^2 + 2a s\), now calculate the initial speed \(u\) for the accident car that skidded \(57.3 \text{ m}\) with deceleration \(a = -8.25 \text{ m/s}^2\): \[v^2 = 0, \quad 0 = u^2 + 2(-8.25)(57.3)\] \[u^2 = 2 \times 8.25 \times 57.3 \approx 947.745\] \[u = \sqrt{947.745} \approx 30.78 \text{ m/s}\]
05

Convert Initial Speed to Miles Per Hour

Convert the calculated speed of the accident car from meters per second back to miles per hour: \[30.78 \text{ m/s} = 30.78 \times \frac{3600}{1609.34} \text{ mi/h} \approx 68.8 \text{ mi/h}\]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Accident Reconstruction
Accident reconstruction is a crucial process in understanding what happened during a vehicle collision. It involves collecting data like skid marks and using physics principles to deduce speeds and forces involved. The length of skid marks can provide insights into how brakes were used and the speed of the vehicle at the time of braking. By analyzing these physical traces, experts can determine if excess speed was a factor in an accident.
This is essential for assessing liability in accidents and improving road safety measures. When conducting accident reconstruction, investigators often reenact scenarios in controlled environments to obtain accurate measurements and compare them to the actual incidents. This helps in validating their findings and ensuring correctness.
Car Deceleration
Deceleration is a decrease in speed over time, crucial in understanding braking events. In physics, it's treated as a negative acceleration. In our example, deceleration occurs when the car's brakes are locked, causing it to skid.
The kinematic equation used to determine deceleration is:
  • \(v^2 = u^2 + 2as\)
'v' represents the final velocity (0 for complete stops), 'u' is the initial velocity, 'a' is acceleration (negative for deceleration), and 's' is the distance over which the deceleration occurs. By rearranging this equation, we can solve for 'a'. The negative result indicates deceleration (\(-8.25 \text{ m/s}^2\) in this case).
Understanding deceleration helps reconstruct accidents and determine whether the car was driving within safe limits before the incident.
Initial Speed Calculation
Calculating a car's initial speed during an incident involves using physics principles and data observed from the accident scene, such as skid mark lengths. This data is plugged into kinematic equations to extract information about initial velocities before accidents.
In our example, knowing the deceleration and the distance the car skidded (from the accident site), we apply the same kinematic formula used for deceleration:
  • \(v^2 = u^2 + 2as\)
Plug in the data: if the final speed \(v\) is 0, 'u' (initial speed) can be solved by rearranging the formula. For the accident car that skidded further than the test (57.3 m compared to 51.5 m), the initial speed is calculated to be \(30.78 \, \text{m/s}\) (about 68.8 mi/h).
This process shows how physics and mathematical calculations can provide clarity about pre-accident conditions, identifying whether excessive speed was a factor.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

\- Two forces act on a \(5.0-\mathrm{kg}\) object sitting on a frictionless horizontal surface. One force is \(30 \mathrm{~N}\) in the \(+x\) -direction, and the other is \(35 \mathrm{~N}\) in the \(-x\) -direction. What is the acceleration of the object?

A hockey puck impacts a goalie's plastic mask horizontally at \(122 \mathrm{mi} / \mathrm{h}\) and rebounds horizontally off the mask at \(47 \mathrm{mi} / \mathrm{h}\). If the puck has a mass of \(170 \mathrm{~g}\) and it is in contact with the mask for \(25 \mathrm{~ms},\) (a) what is the average force (including direction) that the puck exerts on the mask? (b) Assuming that this average force accelerates the goalie (neglect friction with the ice), with what speed will the goalie move, assuming she was at rest initially and has a total mass of \(85 \mathrm{~kg}\) ?

At the end of most landing runways in airports, an extension of the runway is constructed using a special substance called formcrete. Formcrete can support the weight of cars, but crumbles under the weight of airplanes to slow them down if they run off the end of a runway. If a plane of mass \(2.00 \times 10^{5} \mathrm{~kg}\) is to stop from a speed of \(25.0 \mathrm{~m} / \mathrm{s}\) on a \(100-\mathrm{m}\) -long stretch of formcrete, what is the average force exerted on the plane by the formcrete?

In moving a 35.0 -kg desk from one side of a classroom to the other, a professor finds that a horizontal force of \(275 \mathrm{~N}\) is necessary to set the desk in motion, and a force of \(195 \mathrm{~N}\) is necessary to keep it in motion at a constant speed. What are the coefficients of (a) static and (b) kinetic friction between the desk and the floor?

A person has a choice while trying to push a crate across a horizontal pad of concrete: push it at a downward angle of \(30^{\circ},\) or pull it at an upward angle of \(30^{\circ} .\) (a) Which choice is most likely to require less force on the part of the person: (1) pushing at a downward angle; (2) pulling at the same angle, but upward; or (3) pushing or pulling shouldn't matter? (b) If the crate has a mass of \(50.0 \mathrm{~kg}\) and the coefficient of kinetic friction between it and the concrete is \(0.750,\) calculate the required force to move it across the concrete at a steady speed for both situations.
See all solutions

Recommended explanations on Physics Textbooks

Nuclear Physics

Read Explanation

Engineering Physics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Waves Physics

Read Explanation

Turning Points in Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.