Jib Crane Force Variation: Statics Homework | 10kN Capacity & 200kg I Beam

[kehler]

Homework Statement

The jib crane is designed for a maximum capacity of 10kN, and its uniform I beam has a mass of 200kg.
a)Plot the magnitude R of the force on the pin A as a function of x through its operating range of x=0.2m to x=3.8m.
b)Determine the minimum value of R and the corresponding value of x

The Attempt at a Solution

Totally stumped on this one. It'll be great if someone could point me in the right direction.
I didn't even think the force would vary with distance :S. Isn't it only the moment about the point that changes? How do I determine the change in force with distance?

 

[minger]

The pin can only resist force in the y-direction due to the definition of a pin. This means that the resultant force at the pin will be the sum of all the forces in the y-direction. Obviously there is a constant -10kN due to the load, however the resultant force in the y-direction at the cable will be a function of the position.

Sum moments about the pin to get the vertical force in the cable. Then sum forces in the y-direction to get the force at the pin. Get three points to see if it's linear, if it is, then use the equation of a line.

 

[piercas]

it is important to approach problems with a systematic and analytical mindset. In this case, we are dealing with a jib crane that has a maximum capacity of 10kN and a uniform I beam with a mass of 200kg. The goal is to plot the magnitude of the force on the pin A as a function of x through its operating range and determine the minimum value of R and the corresponding value of x.

First, let's define some variables and parameters that will be useful in our analysis. Let x represent the distance from the pivot point A to the end of the jib crane, and let R represent the force on the pin A. We can also define the weight of the I beam as W, and the maximum capacity of the crane as F_max.

Now, we can start by considering the forces acting on the jib crane. At any given distance x, we have the weight of the I beam acting downwards and the force R acting upwards at the pin A. We can also consider the moment about the pivot point A, which is given by the product of the force R and the distance x.

Using Newton's second law, we can write the following equation for the forces in the vertical direction:

R - W = 0

Since we know that the weight of the I beam is equal to its mass times the acceleration due to gravity (W = mg), we can substitute this into the equation and solve for R:

R = mg = 200kg * 9.8m/s^2 = 1960N

This means that at any given distance x, the force on the pin A will be 1960N, which is the minimum value of R.

To determine the maximum value of R, we need to consider the moment equation. We know that the maximum capacity of the crane is 10kN, which means that the moment at the pivot point A cannot exceed this value. We can write the following equation:

Rx = F_max

Solving for R, we get:

R = F_max / x = 10kN / x

This means that the maximum value of R will occur at the minimum distance x, which is 0.2m. Therefore, the maximum value of R is 10kN / 0.2m = 50kN.

To plot the magnitude of R as a function of x, we can use these values to create a graph. The graph