Chapter 11, Problem 023 LI Your answer is partially correct. Try again. Force F

Question

Chapter 11, Problem 023 LI Your answer is partially correct. Try again. Force F (9.01 N )i- 3.75 N k acts on a pebble with position vector r (7.51 m)j- 2.33 m k relative to the origin. What is the resulting torque acting on the pebble about (a) the origin and (b) a point with coordinates (8.32 m, 0, -3.08 m)? Unit TN m (a) Number T-28.16 -2.33 k Units (b) Number click if you would like to show work for this question Open Show Work SHOW HINT LINK TO SAMPLE PROBLEM ULINK TO SAMPLE PROBLEM LINK TO SAMPLE PROBLEM LINK TO SAMPLE PROBLEM MATH HELP LINK TO TEXT Question Attempts: 1 of 4 used SAVE FOR LATER SUBMIT ANSWER Version 4.22.2.9 ns, Inc. All Rights Reserved. A Division of John Wiley & Sons, Inc 6:59 PM 4/18/2017

Explanation / Answer

We have F = (9.01N)i - (3.75N)k

and position vector of the pebble is given by:

r = (7.51m)j - (2.33m)k

     

a) Torque about origin on the pebble is given by:

T = rxF = [(7.51 m)j - (2.33 m)k]X[(9.01 N)i - (3.75 N)k]

or T = -(67.66 N-m)k - (20.99 N-m)j - (28.16 N-m)i

or T = - (28.16 N-m)i - (20.99 N-m)j - (67.66 N-m)k

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b) Here we have to find out the torque on the pebble about a point with coordinates (8.32 m, 0, -3.08 m).

Position vector of this point is r1 = (8.32 m)i - (3.08 m)k

Now, torque T = (r - r1)xF

Now, r - r1 =  (7.51 m)j - (2.33 m)k - [(8.32 m)i - (3.08 m)k] = - (8.32 m)i +  (7.51 m)j + (0.75 m)k

So,  r - r1 = - (8.32 m)i +  (7.51 m)j + (0.75 m)k

Thus,

T =  (r - r1)xF

= [- (8.32 m)i +  (7.51 m)j + (0.75 m)k]X[(9.01N)i - (3.75N)k]

= -(31.2 N-m)j - (67.66 N-m)k - (28.16 N-m)i + (6.75N-m)j

= -(28.16 N-m)i - (24.45 N-m)j - (67.66 N-m)k

So, the torque is:

T = -(28.16 N-m)i - (24.44 N-m)j - (67.66 N-m)k

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