What is the magnitude of F required to raise the lamp post?

[celtics777]

Homework Statement

In order to raise the lamp post from the position shown, the force on the cable must create a counterclockwise moment of 1500 lb*ft about point A. Determine the magnitude of F that must be applied to the cable.

Homework Equations

I can find the magnitude of a vector when I know the vector. Not in this problem.

The Attempt at a Solution

I know a fair amount to get started, such as definitions, but I have no idea how to actually do calculations.

 

[PhanthomJay]

Are you familiar with the cross product rule for determining moments?

 

[celtics777]

I'm familiar with the cross product, but not sure how to use it to determine moment.

 

[PhanthomJay]

M = r X F =rFsintheta, wher r is the magnitude of the position vector between the base of the post and the point of application of the force(the length of the post), F is the magnitude of the applied tensile force, ant theta is the included angle between the force and position vectors. You'll have to use the law of sines and cosines to first find theta.

 

[rezeew]

I would approach this problem by first identifying the relevant physical principles and equations that can help us solve for the unknown magnitude of F. In this case, we can use the concept of torque, which is the product of force and distance from the pivot point, to determine the magnitude of F.

First, we can set up the equation for torque as T= F*d, where T is the torque, F is the force applied, and d is the distance from the pivot point. In this case, we know that the torque is 1500 lb*ft and the distance d is unknown. Therefore, we can rearrange the equation to solve for F as F= T/d.

Next, we need to determine the distance d. Looking at the diagram, we can see that the distance from point A to the point where the force is applied is the same as the length of the cable. Therefore, we can use the Pythagorean theorem to find the length of the cable, which is the hypotenuse of a right triangle formed by the lamp post and the ground. This can be expressed as d= √(20^2 + 10^2) = √500 = 22.36 ft.

Now, we can plug in the known values into the equation F= T/d to solve for the magnitude of F. This gives us F= 1500 lb*ft/22.36 ft = 67.1 lb.

Therefore, the magnitude of F that must be applied to the cable to raise the lamp post is approximately 67.1 lb.