Chapter 14 Skill Building

# Chapter 14 Skill Building - MasteringPhysics: Assignment...

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MasteringPhysics: Assignment Print View Vector Cross Product Let vectors , , and . Calculate the following, expressing your answers as ordered triples (three comma-separated numbers). Part A Hint A.1 The cross product Hint not displayed ANSWER: = 15.0,5.00,5.00 Part B ANSWER: = - 15.0, - 5.00, - 5.00 Part C ANSWER: = 4.00,5.00, - 17.0 Part D ANSWER: = 24.0,30.0, - 102 Part E ANSWER: = 15.0,5.00,5.00 Part F ANSWER: = 55.0

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MasteringPhysics: Assignment Print View and are different vectors with lengths and respectively. Find the following, expressing your answers in terms of given quantities. Part G Hint G.1 What is the angle between a vector and itself? Hint not displayed Hint G.2 Magnitude of the cross product Hint not displayed ANSWER: = 0 Part H If and are perpendicular, Hint H.1 What is the angle between perpendicular vectors? Hint not displayed Hint H.2 Magnitude of the cross product Hint not displayed ANSWER: = Part I If and are parallel, Hint I.1 What is the angle between two parallel vectors? Hint not displayed ANSWER: = 0 Finding the Cross Product
MasteringPhysics: Assignment Print View The figure shows two vectors and separated by an angle . You are given that , , and . Part A Express as an ordered triplet of values, separated by commas. ANSWER: = 0,0,10.0 Part B Find the magnitude of . ANSWER: = 10.0 Part C Find the sine of the angle between and . ANSWER: = 0.707 Hoop on a Ramp A circular hoop of mass , radius , and infinitesimal thickness rolls without slipping down a ramp inclined at an angle with the horizontal.

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MasteringPhysics: Assignment Print View Part A What is the acceleration of the center of the hoop? Hint A.1 How to approach the problem Hint not displayed Part A.2 Find the torque about the center of mass Part not displayed Part A.3 Find an expression for the torque Part not displayed Part A.4 What is the moment of inertia of the hoop? Part not displayed Part A.5 Find the frictional force Part not displayed Part A.6 Find the linear acceleration Part not displayed Hint A.7 Hint not displayed Express the acceleration in terms of physical constants and all or some of the quantities , , and . ANSWER: = So the acceleration is independent of the hoop characteristics, that is, the mass and size (radius) of the hoop. This is quite generally true for objects freely rolling down a ramp; the acceleration depends only on the distribution of mass, for example, whether the object is a disk or a
MasteringPhysics: Assignment Print View sphere, but within each class the acceleration is the same. For example, all spheres will accelerate at the same rate, though this rate is different from the rate for (all) disks. Part B What is the minimum coefficient of (static) friction needed for the hoop to roll without slipping? Note that it is static and not kinetic friction that is relevant here, since the bottom point on the wheel is not moving relative to the ground (this is the meaning of no slipping).

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## This homework help was uploaded on 04/08/2008 for the course PEP 111 taught by Professor Whittaker during the Fall '07 term at Stevens.

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Chapter 14 Skill Building - MasteringPhysics: Assignment...

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