Exam question problem: moments

[Taylor_1989]

Homework Statement

I am having problem calculating this question. I even looked at the answer sheet and worked back, which gave me some luck, but still do not fully grasp the question.(i) Calculate the weight W of the workman.

Homework Equations

moment clockwise = moment anticlockwise

The Attempt at a Solution

My attempt pre look at question: I did 0.20-0.03= 0.17, 0.20+0.03= 0.23 so far so good.
I the did 0.20+0.50=0.70 so middle Q which then gave me 0.67 and 0.73. I then took the W*0.17=160*0.73.

But when I looked at the answer I got the first part right but the second part wrong. Do I have to include R and S into the equation? I would appreciate the help if possible.

Also here is what the answer says: W × 0.17/0.20/0.23 = 160 × 0.72/0.75/0.78
W × 0.17 = 160 × 0.78 or 600 N
730/734 N

I really can't see where the 0.72 ect come from unless you included distance from R S but the weight is in the middle.

 

[tms]

The first thing to do, for this and all problems, is to solve it symbolically; forget there are numbers until the very last step. You'll never learn the physics if you plug in numbers from the beginning.

Second, your "relevant equation" is not only ambiguous (what moment are you talking about), it is wrong. The system is in equilibrium, so the net force is zero and the net torque is also zero. That is your starting point. Write down those equations, then solve for W.

 

[Taylor_1989]

The first thing to do, for this and all problems, is to solve it symbolically; forget there are numbers until the very last step. You'll never learn the physics if you plug in numbers from the beginning.

Second, your "relevant equation" is not only ambiguous (what moment are you talking about), it is wrong. The system is in equilibrium, so the net force is zero and the net torque is also zero. That is your starting point. Write down those equations, then solve for W.

could you please expand, I really can't see where you are coming from. I have looked in my study books and the point me in the directions of levers and moments.

 

[tms]

The torque of the man plus his segment of the board and the torque of the rest of the board must be equal. Recall that [itex]\mathbf\tau = \mathbf{r} \times \mathbf{F}[/itex]. Since the angles of both torques are 90 degrees, this reduces to [itex]\tau = rF[/itex].

 

[asteriatic]

Dear student,

Thank you for reaching out for help with this question. Moments can be a tricky concept to grasp, but I'm here to help you understand it better.

First, let's start by defining what a moment is. A moment is a turning force caused by a force acting at a distance from a pivot point. In this question, the pivot point is the middle of the beam, and the forces acting on it are the weight of the workman and the weight of the beam itself.

Now, let's break down the steps to solve this question:

1. Draw a diagram: Drawing a diagram can help you visualize the problem better. Draw a beam with two forces acting on it - the weight of the workman (W) and the weight of the beam (B).

2. Identify the pivot point: As mentioned earlier, the pivot point is the middle of the beam.

3. Set up the equation: The key to solving this problem is understanding that the sum of the clockwise moments is equal to the sum of the anticlockwise moments. This is known as the principle of moments. So, we can set up the equation as follows:

(W*0.17) = (B*0.03) + (B*0.23)

4. Solve for W: Now, we have one equation and one unknown (W). We can solve for W by rearranging the equation as follows:

W = (B*0.03 + B*0.23)/0.17

5. Substitute values: We can now substitute the values given in the question: B = 160 N and W = 600 N. This gives us:

600 = (160*0.03 + 160*0.23)/0.17

6. Solve for B: We can now solve for B by rearranging the equation as follows:

B = (600*0.17)/0.3 = 340 N

Therefore, the weight of the workman is 600 N and the weight of the beam is 340 N.

I hope this explanation helps you understand the concept of moments better. Remember, drawing a diagram and setting up the equation correctly are key to solving any moment problem. Keep practicing and you will get the hang of it.

Best of luck with your studies!

Sincerely,