Line of action for which the resultant force of the wrench passes

[imd]

In tightening a bolt whose center is at point O, a person exerts a 180-N force on the ratchet handle with his right hand. In addition, with his left hand he exerts a 90-N force as shown in order to secure the socket onto the bolt head. Determine the equivalent force–couple system at O. Then find the point in the x-y plane through which the line of action of the resultant force of the wrench passes.

The answer should be:

R = -90j - 180k N

M = -6.3i - 36j N*m
x = -160 mm

y = 35 mm

 

[BvU]

And what is your question ?

 

[imd]

Sorry I did not specify. I am not sure how to solve the problem, I can find the Force and Moment around O but cannot find the line of action on x. If you could briefly explain how to do the problem that would be great. Thanks!

 

[BvU]

Ah, that clears some of the fog. Next time use the template (read the guidelines to find out why it's compulsory in PF).
And: welcome to PF :) !

Not exactly as described in the guidelines, but I can now at least estimate you are able to sort out what is given and you can convert at least some of what is asked into something to do. I hope that's also true if the answer isn't in the back of the book.

Now comes the bummer: I have no idea either where the -160 comes from ! Resultant force link doesn't help me: there is nothing in the x or -x direction I can find. Almost want to ask: could this be a typo ?

But perhaps someone else listening in has a better idea ?

 

[HalfLostAndSearching]

I would first analyze the given information and draw a diagram to better understand the situation. From the given forces, the equivalent force-couple system at point O can be calculated using the equations R = F1 + F2 and M = r x F. Using the values given, the resultant force R and the moment M can be calculated to be -90j - 180k N and -6.3i - 36j N*m, respectively.

To determine the point in the x-y plane through which the line of action of the resultant force of the wrench passes, I would use the equation M = r x F. By setting M = 0, we can solve for the point where the line of action of the resultant force passes through. Using the values calculated above, we can solve for the point to be at (-160 mm, 35 mm) in the x-y plane.

This information can be useful in understanding the forces and moments acting on the bolt and the importance of properly securing the socket onto the bolt head. It also highlights the importance of considering the point of application of forces in any mechanical system. Further analysis and calculations can be done to determine the stability and effectiveness of the wrench in tightening the bolt.