Replace the system of two forces and once couple by a Wrench

[Northbysouth]

*The title for this question is incorrect. I messed it up with another question. My apologies.

Homework Statement

Replace the system of two forces and one couple shown in Prob. 2/158 by a wrench. Determine the magnitude of the moment M of the wrench, the magnitude of the force R of the wrench, and the coordinates of the point P in the x-y plane through which the wrench passes.

Homework Equations

The Attempt at a Solution

I found the magnitude of the resultant to be:

R_x = -49 kN
R_y = -35*sin(69.04) = -32.684
R_z = 35*cos(69.04)

R = 60.216 kN

I'm fairly sure that this value is correct but I am not sure

Then for the moment I got:

M_x = -35*cos(20.956)*1.8m + 35sin(20.956)(4.7m) = 0
M_y = 49*1.8m = 88.2 kNm
M_z -36 kNm

M = 95.264 kNm

But it says this answer is wrong.

From this point I am unsure how to find the location of the x and y coordinate

All help would be appreciated

 

[KataKoniK]

.Hello,

I apologize for the mistake in the title of this question. Can you please clarify what you are looking for in terms of a wrench? Are you trying to find the equivalent wrench that can replace the system of forces and couple shown in Prob. 2/158? If so, can you provide more information about the system and the wrench you are trying to find?

In terms of your attempt at solving the problem, your calculations for the resultant force seem correct. However, for the moment, it seems like you have mixed up the units for the distance and force. The units for moment are usually Nm or kNm, and the units for force are N or kN. So, your moment values should be in kNm as well. Additionally, you have only calculated the moment components in the x and y directions, but you need to also consider the z direction. The moment vector can be found by taking the cross product of the force and distance vectors. So, your final moment value should be a vector, not just a scalar value.

To find the location of the x and y coordinates, you can use the equations for moment equilibrium. Since the system is in equilibrium, the sum of all moments about any point should be equal to zero. So, you can choose a point (x,y) and set up equations for the moments in the x and y directions, and solve for the unknown coordinates.

I hope this helps. Please let me know if you need further clarification.