Determine the coordinaes of the x-y plane through which the wrench passes

[Northbysouth]

Homework Statement

In tightening a bolt whose center is at point O, a person exerts a 56-lb force on the ratchet handle with his right hand. In addition, with his left hand he exerts a 10-lb 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 wrench passes.

Imaged attached

Homework Equations

The Attempt at a Solution

I calculated the resultant and moment as follows:

R_x = 0
R_y = -10 lb
R_z = -56 lb

M_x = (-56lb)(2.1 inches) = -117.6 ln-in
M_y = (-56 lb)(6.5 inches) = -364 lb in
M_z = 0

I fairly certain that the above values are correct. My confusion is with calculating the point on the x-y plane through which the line of action passes. I would appreciate any help. Thanks

 

[KataKoniK]

.
Thank you for your post. It looks like you have correctly calculated the resultant force and moment at point O. To determine the point on the x-y plane through which the line of action of the wrench passes, you can use the following equation:

Mx = Fy*dz - Fz*dy

Where:
Mx = moment about the x-axis
Fy = force in the y-direction
dz = distance from the point of interest to the z-axis
Fz = force in the z-direction
dy = distance from the point of interest to the y-axis

Since we know the values for Mx, Fy, and Fz from your calculations, we can rearrange the equation to solve for dz:

dz = (Mx + Fz*dy)/Fy

Plugging in the values, we get:

dz = (-117.6 ln-in + 56 lb * 6.5 inches)/(-10 lb) = 7.76 inches

Therefore, the point on the x-y plane through which the line of action of the wrench passes is 7.76 inches away from the z-axis.

I hope this helps. Let me know if you have any further questions.