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High School Math Calculus Precalculus with Limits: A Graphing Approach

The expression for torque T on the crank as a function of p if the magnitude of the torque on the crank is ‖ V × F ‖ .

The expression for torque T on the crank as a function of p if the magnitude of the torque on the crank is ‖ V × F ‖ .

Precalculus with Limits: A Graphing Approach

Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

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Question

Chapter 10.3, Problem 63E

(a)

To determine

To find: The expression for torque T on the crank as a function of p if the magnitude of the torque on the crank is ‖V×F‖ .

(a)

Expert Solution

Answer to Problem 63E

The expression for torque T on the crank as a function of p is ‖V×F‖=p2cos40° .

Explanation of Solution

Given information:

The position of the crank is V=12(cos40°j+sin40°k) and the force is F=−pk .

Calculation:

Consider the cross product.

V×F=|ijk012cos40°12sin40°00−p|=|12cos40°12sin40°0−p|i−|012sin40°0−p|j+|012cos40°00|k=−p2cos40°i−0j+0k=−p2cos40°i

Find the absolute value.

‖V×F‖=||−p2cos40°i||T=‖V×F‖=p2cos40°

Therefore, the expression for torque T on the crank as a function of p is ‖V×F‖=p2cos40° .

(b)

To determine

To complete: The given table.

(b)

Expert Solution

Answer to Problem 63E

The complete table is shown below.

Explanation of Solution

Given information:

From part (a), the expression for the torque is T=‖V×F‖=p2cos40° .

The given table is shown below.

p	15	20	25	30	35	40	45
T

Calculation:

From part (a), the expression for the torque is T=‖V×F‖=p2cos40° . Substitute the values of p for the different value of torque T .

The complete table is shown below.

p	15	20	25	30	35	40	45
T	5.75	7.66	9.58	11.49	13.41	15.32	17.24

Therefore, the complete table is shown above.

Chapter 10.3, Problem 62E

Chapter 10.3, Problem 64E

Chapter 10 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

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