Need some help with TENSION (problems 3 & 4 in the pdf)

[silentcascade]

Homework Statement

PROBLEM 3: A staging that weighs 290 N supports two painters, one 430 N and the other 490 N. The reading in the left scale is Fl = 500 N. What is the reading Fr in the right hand
scale? Further description is the picture in the pdf.

PROBLEM 4:So basically in problem 4, there is a 56 N weight suspended in the air by two ropes. One of the ropes is slanted at 53 degrees to the ceiling, and the other rope is perpendicular to the wall. Both intersect and join at a point and then descend vertically as one rope attached to the weight. If you need any more visual descriptions, a picture is included in the pdf.

Homework Equations

PROBLEM 3: soh cah toa (sin=opposite/hypotenuse, cos=adjacent/hypotenuse, and tangent=opposite/adjacent)

PROBLEM 4: soh cah toa (sin=opposite/hypotenuse, cos=adjacent/hypotenuse, and tangent=opposite/adjacent)

The Attempt at a Solution

PROBLEM 3: So I knew the total downward force of the staging and the painters combined: 430 N+490 N+290 N= 1210 N. And if the reading on the scale was 500 N on the left side (assuming 430 N is also on the left side), then that means that the upward force from the right rope was 220 N. I don't know how to solve this.

PROBLEM 4: I basically extended the vertical rope until it hit the ceiling, so the section between the horizontal and the diagonal ropes was split into a right triangle and a rectangle. I figured that the theta of the right triangle was 37 (90-53) and then used sin (37) to get 0.6018150231520482799179770004414898414256377. This gave me the ratio of two lengths that I didn't know. I then moved on to find the forces. So if the force on the block was 56 N, that mean that the adjacent of the right triangle would have to be equal to that because the block was in equilibrium. Now i just don't know what to do next.

Thank you for reading! Oh, please help, by the way.

 

[anathema]

Hello there,

For PROBLEM 3, you are on the right track. You correctly found the total downward force of the staging and painters combined, which is 1210 N. Since the reading on the left scale is 500 N, that means the upward force from the right rope must be 710 N (1210 N - 500 N). This is because the total upward force must be equal to the total downward force for the staging to be in equilibrium.

Now, to find the reading on the right scale, you can use the Pythagorean theorem. The right rope forms a right triangle with the vertical and horizontal ropes. The vertical rope has a length of 710 N (upward force from the right rope) and the horizontal rope has a length of 430 N (weight of one painter). You can use the Pythagorean theorem to find the length of the right rope, which will give you the reading on the right scale.

For PROBLEM 4, you are also on the right track. You correctly found the ratio of the two lengths using sin(37). Now, you can use this ratio to find the lengths of the two sections of the horizontal rope. The length of the horizontal rope must be equal to the weight of the block (56 N). Once you have the lengths of the two sections of the horizontal rope, you can use the Pythagorean theorem to find the tension in each rope (since they form right triangles with the vertical rope). The sum of the tensions in the two ropes must be equal to the weight of the block for it to be in equilibrium.

I hope this helps! Let me know if you need further clarification or assistance. Good luck with your homework!