Calculate the Support Reactions at A and B as a Result of the Force

[Northbysouth]

Homework Statement

The load per foot of beam length varies as shown. For x = 17 ft, the unit load is 373 lb/ft. At x = 0, the load is increasing at the rate of 41 lb/ft per foot. Calculate the support reactions at A and B. The reactions are positive if upward, negative if downward.

I have attached an image of the question.

Homework Equations

The Attempt at a Solution

I know that I need to integrate the function, w = k₁x - k₂x² but I'm not sure how to find the variable k₁ and k₂. Plugging in the information that when x = 17, w = 373 I get

373 = 17k₁ - 289k₂

But I'm not sure how to proceed from here. I realize that it also says that when x = 0 the load is increasing at a rate of 41 lb/ft but I'm not certain how I should interpret this.

Help would be appreciated. Thank you

 

[lewando]

From the equation, when x=0, w=0. And you are given the slope at (0,0). So you have 2 points and a slope at one of those points. I think that is sufficient to find the constants k1 and k2.

 

[Northbysouth]

Oh, I've got it now. I just take the derivative of the function, then I can solve for k1 and k2.

Thank you.