Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Question
Chapter 11, Problem 4P
To determine
To prove: The equation 11.7 given in the textbook.
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Check out a sample textbook solutionStudents have asked these similar questions
Use the definition of the vector product and the defini-
tions of the unit vectors î, j, and k to prove Equations 11.7.
You may assume the x axis points to the right, the y axis
up, and the z axis horizontally toward you (not away from
you). This choice is said to make the coordinate system a
right-handed system.
î x i = j x j = k x k = 0
i xj = -j x î = k
jx k = -k x j = i
k x i= - i x k = }
The cross product
AxB
is perpendicular to both vectors in the cross product (think of Aand
В
as lying on a
sheet of paper; the cross product is perpendicular to the plane of the sheet).
After figuring out the two directions perpendicular to both vectors you use one of the right hand rules given
on Page 338 to choose which of the two direction is correct. All three should give the same result so use
whichever one you are most comfortable with. In class, we will use the middle one in the diagram in the book.
The vector torque is
where "is the vector from the axis of rotation to where the force is applied.
Which is the direction of the torque vector?
+y
++
* (in)
+z (out)
O = in
(O) = out
You are given 3 vectors: p = j - 3k, q = -2i - j - 3k and r = 4i + j + 3k. You are informed that these three vectors are Cartesian unit vectors.
To answer this question, use the following vector form:
a1i + a2j + a3k
Write down the sum of the vectors s = p + q + r
And then calculate the scaler product of s x r
Chapter 11 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 11.1 - Which of the following statements about the...Ch. 11.2 - Recall the skater described at the beginning of...Ch. 11.3 - A solid sphere and a hollow sphere have the same...Ch. 11.4 - A competitive diver leaves the diving board and...Ch. 11 - Prob. 1PCh. 11 - The displacement vectors 42.0 cm at 15.0 and 23.0...Ch. 11 - Prob. 3PCh. 11 - Prob. 4PCh. 11 - Two forces F1 and F2 act along the two sides of an...Ch. 11 - A student claims that he has found a vector A such...
Ch. 11 - A particle is located at a point described by the...Ch. 11 - A 1.50-kg particle moves in the xy plane with a...Ch. 11 - Prob. 9PCh. 11 - Heading straight toward the summit of Pikes Peak,...Ch. 11 - Review. A projectile of mass m is launched with an...Ch. 11 - Prob. 12PCh. 11 - A particle of mass m moves in a circle of radius R...Ch. 11 - A 5.00-kg particle starts from the origin at time...Ch. 11 - A ball having mass m is fastened at the end of a...Ch. 11 - Prob. 16PCh. 11 - A uniform solid disk of mass m = 3.00 kg and...Ch. 11 - Show that the kinetic energy of an object rotating...Ch. 11 - Prob. 19PCh. 11 - Prob. 20PCh. 11 - Prob. 21PCh. 11 - Prob. 22PCh. 11 - A 60.0-kg woman stands at the western rim of a...Ch. 11 - Prob. 24PCh. 11 - A uniform cylindrical turntable of radius 1.90 m...Ch. 11 - Prob. 26PCh. 11 - A wooden block of mass M resting on a...Ch. 11 - Prob. 28PCh. 11 - A wad of sticky clay with mass m and velocity vi...Ch. 11 - A 0.005 00-kg bullet traveling horizontally with a...Ch. 11 - The angular momentum vector of a precessing...Ch. 11 - A light rope passes over a light, frictionless...Ch. 11 - Prob. 33APCh. 11 - Prob. 34APCh. 11 - We have all complained that there arent enough...Ch. 11 - Prob. 36APCh. 11 - A rigid, massless rod has three particles with...Ch. 11 - Prob. 38APCh. 11 - Two astronauts (Fig. P11.39), each having a mass...Ch. 11 - Two astronauts (Fig. P11.39), each having a mass...Ch. 11 - Native people throughout North and South America...Ch. 11 - Two children are playing on stools at a restaurant...Ch. 11 - You are attending a county fair with your friend...Ch. 11 - Prob. 44APCh. 11 - Global warming is a cause for concern because even...Ch. 11 - The puck in Figure P11.46 has a mass of 0.120 kg....Ch. 11 - Prob. 47APCh. 11 - A solid cube of wood of side 2a and mass M is...Ch. 11 - Prob. 49CPCh. 11 - Prob. 50CP
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- Show that when A+B=C then A2+B2+2ABcos , where is the angle between vectors A and B .arrow_forwardGiven a vector A=4.5+4.5j and a vector B=4.5+4.5j, determine the magnitude of the cross product of these two vectors, AB. Hint: Make a sketch of both vectors including a coordinate system.arrow_forwardFind the angle between vectors for (a) D=(-3.0i-4.0j)m and A=(-3.0i+4.0j)m and (b) D=(2.0i+4.0j+K)m and B=(-2.0i+3.0j+2.0K)m .arrow_forward
- Find for the Cross Product of the following pairs of vectors 1. A=4i-5j +8k, B = -2i+3j+3k 2. C = -6i+4j+7k, D=4i-j+5k 3. E= -i-5j + 2k, F = 8i+2j-6karrow_forwardProblem 4: It should be obvious that the magnitude of a vector is independent of the choice of coordinate system. This implies that r r is the same for any set of axes. Use this to prove that the dot product of two different vectors r.s is also independent of coordinate system. [Hint: Consider the length of r + s.]arrow_forwardCalculate the magnitude of the cross product of the following two vectors: b = 2j + 5k = (0 ,2,5) å = 1î + 3ĵ = (1,3,0) , b= 2ĵ + 5k = (0 ,2 , 5)arrow_forward
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