Example 11.2 The Torque Vector A force of F = (4.00i + 7.00f) N is applied to an object that is pivoted about a fixed axis aligned along the z coordinate axis. The force is applied at a point located at i= (5.00i + 6.00j) m. Find the torque applied to the object. SOLVE IT Conceptualize Given the unit-vector notations, think about the directions of the force and position vectors. If this force were applied at this position, in what direction would an object pivoted at the origin turn? Categorize Because we use the definition of the cross product discussed in this section, we categorize this example as a substitution problem. Set up the torque vector using the following equation: # = ixF = [(5.00i + 6.00j) m] x [(4.00i + 7.009) N] 7 = [(5.00)(4.00)i xi + (5.00)(7.00)î xĵ + (6.00)(4.00)j x i - (6.00)(7.00)j x j] N - m Perform the multiplication: Evaluate the various terms: 7 = [0 + 35k + -24k + 0] N - m = [11 kN - m Notice that bothr and F are in the xy plane. As expected, the torque vector is perpendicular to this plane, having only a z component. MASTER IT HINTS: GETTING STARTED I I'M STUCK! Suppose the same magnitude force is applied at the same point as in the example, and the torque is found to have the same magnitude but in the opposite direction of the torque found there. What are the components of the force? + 13 x i) N Consider how sign changes can be made to result Enter a number. in the vector produc. by changes in the vector components, and what kind of changes in vector components leave the magnitude of the vector unaffected. Apply this to the present problem.
Example 11.2 The Torque Vector A force of F = (4.00i + 7.00f) N is applied to an object that is pivoted about a fixed axis aligned along the z coordinate axis. The force is applied at a point located at i= (5.00i + 6.00j) m. Find the torque applied to the object. SOLVE IT Conceptualize Given the unit-vector notations, think about the directions of the force and position vectors. If this force were applied at this position, in what direction would an object pivoted at the origin turn? Categorize Because we use the definition of the cross product discussed in this section, we categorize this example as a substitution problem. Set up the torque vector using the following equation: # = ixF = [(5.00i + 6.00j) m] x [(4.00i + 7.009) N] 7 = [(5.00)(4.00)i xi + (5.00)(7.00)î xĵ + (6.00)(4.00)j x i - (6.00)(7.00)j x j] N - m Perform the multiplication: Evaluate the various terms: 7 = [0 + 35k + -24k + 0] N - m = [11 kN - m Notice that bothr and F are in the xy plane. As expected, the torque vector is perpendicular to this plane, having only a z component. MASTER IT HINTS: GETTING STARTED I I'M STUCK! Suppose the same magnitude force is applied at the same point as in the example, and the torque is found to have the same magnitude but in the opposite direction of the torque found there. What are the components of the force? + 13 x i) N Consider how sign changes can be made to result Enter a number. in the vector produc. by changes in the vector components, and what kind of changes in vector components leave the magnitude of the vector unaffected. Apply this to the present problem.
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)...
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![Example 11.2
The Torque Vector
A force of F = (4.00i + 7.00f) N is applied to an object that is pivoted about a fixed axis aligned along
the z coordinate axis. The force is applied at a point located at i= (5.00i + 6.00j) m. Find the torque
applied to the object.
SOLVE IT
Conceptualize Given the unit-vector notations, think about the directions of the force and position
vectors. If this force were applied at this position, in what direction would an object pivoted at the origin
turn?
Categorize Because we use the definition of the cross product discussed in this section, we categorize
this example as a substitution problem.
Set up the torque vector using the
following equation:
# = ixF = [(5.00i + 6.00j) m] x [(4.00i + 7.009) N]
7 = [(5.00)(4.00)i xi + (5.00)(7.00)î xĵ
+ (6.00)(4.00)j x i - (6.00)(7.00)j x j] N - m
Perform the multiplication:
Evaluate the various terms:
7 = [0 + 35k + -24k + 0] N - m = [11
kN - m
Notice that bothr and F are in the xy plane. As expected, the torque vector is perpendicular to this
plane, having only a z component.
MASTER IT
HINTS:
GETTING STARTED I I'M STUCK!
Suppose the same magnitude force is applied at the same point as in the example, and the torque is
found to have the same magnitude but in the opposite direction of the torque found there. What are the
components of the force?
+ 13
x i) N Consider how sign changes can be made to result
Enter a number.
in the vector produc. by changes in the vector components, and what kind of changes in vector
components leave the magnitude of the vector unaffected. Apply this to the present problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99269e07-9031-4b41-ba3f-5f1d3d15b266%2F8daf0a68-6b4c-4bf0-92d9-d2f5272f6a83%2F1mlojb9.png&w=3840&q=75)
Transcribed Image Text:Example 11.2
The Torque Vector
A force of F = (4.00i + 7.00f) N is applied to an object that is pivoted about a fixed axis aligned along
the z coordinate axis. The force is applied at a point located at i= (5.00i + 6.00j) m. Find the torque
applied to the object.
SOLVE IT
Conceptualize Given the unit-vector notations, think about the directions of the force and position
vectors. If this force were applied at this position, in what direction would an object pivoted at the origin
turn?
Categorize Because we use the definition of the cross product discussed in this section, we categorize
this example as a substitution problem.
Set up the torque vector using the
following equation:
# = ixF = [(5.00i + 6.00j) m] x [(4.00i + 7.009) N]
7 = [(5.00)(4.00)i xi + (5.00)(7.00)î xĵ
+ (6.00)(4.00)j x i - (6.00)(7.00)j x j] N - m
Perform the multiplication:
Evaluate the various terms:
7 = [0 + 35k + -24k + 0] N - m = [11
kN - m
Notice that bothr and F are in the xy plane. As expected, the torque vector is perpendicular to this
plane, having only a z component.
MASTER IT
HINTS:
GETTING STARTED I I'M STUCK!
Suppose the same magnitude force is applied at the same point as in the example, and the torque is
found to have the same magnitude but in the opposite direction of the torque found there. What are the
components of the force?
+ 13
x i) N Consider how sign changes can be made to result
Enter a number.
in the vector produc. by changes in the vector components, and what kind of changes in vector
components leave the magnitude of the vector unaffected. Apply this to the present problem.
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