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# A car starts rolling down a 1 -in-4 hill (1 -in-4 means ISBN: 9780130606204 3

## Solution for problem 71GP Chapter 4

Physics: Principles with Applications | 6th Edition

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Problem 71GP

Problem

A car starts rolling down a 1 -in-4 hill (1 -in-4 means that for each 4 m traveled along the sloping road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction. (h) Assume an effective coefficient of friction equal to 0.10.

Step-by-Step Solution:

Solution 71GP: We have to determine the velocity of the car as it is reaches the of the hill in presence and absence of friction. Step 1 of 8 Concept: Newton’s second law: The net force F acting on an object of mass m produces an acceleration a in that object. Mathematically, F= ma. Free body diagram of a body gives the diagrammatical representation of all the forces acting on the body in terms of magnitude and diagram, under the given situation. The kinematic equation relating the initial velocity (u)and final velocity (v) of an object, accelerating by an acceleration (a), having its displacement (s) is given as, v = u + 2as Step 2 of 8 FIgure below shows the free body diagram of the moving car. m Mass of the car mg Weight of the car acting vertically downward due to gravity Angle made by the inclined surface with the horizontal F frFrictional force acting between the car and surface N Normal reaction exerted by the ground on the car s Distance covered while reaching the bottom = 55 m Step 3 of 8 For simplification of calculation resolving the weight into two components, mgsin Component of weight acting along the plane mgcos Component of weight acting perpendicular to the plane Also, distance covered while reaching the bottom s = 55 m For each 4.0 m horizontal distance covered by the car along the hill, the elevation in the hill is 1.0 m. Therefore, the angle made by the surface with the horizontal is 1 sin = 4 1 1 = sin 4 o = 14.5 o Angle made by the inclined surface with the horizontal is = 14.5 . Step 4 of 8 A] Assuming the friction is absent If friction is not present the only component of weight responsible for accelerating the car down the hill would be mgsin.Using Newton’s second law, we get, ma = mg sin a = g sin a = 9.8 ×sin 14.5 o a = 9.8 ×sin 14.5 o a = 2.45 m/s 2 Acceleration of the car down the hill, in absence of friction, is a = 2.45 m/s2

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##### ISBN: 9780130606204

The full step-by-step solution to problem: 71GP from chapter: 4 was answered by , our top Physics solution expert on 03/03/17, 03:53PM. The answer to “A car starts rolling down a 1 -in-4 hill (1 -in-4 means that for each 4 m traveled along the sloping road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction. (h) Assume an effective coefficient of friction equal to 0.10.” is broken down into a number of easy to follow steps, and 55 words. This full solution covers the following key subjects: Friction, along, bottom, Car, change. This expansive textbook survival guide covers 35 chapters, and 3914 solutions. This textbook survival guide was created for the textbook: Physics: Principles with Applications, edition: 6. Physics: Principles with Applications was written by and is associated to the ISBN: 9780130606204. Since the solution to 71GP from 4 chapter was answered, more than 755 students have viewed the full step-by-step answer.

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