In Fig. 12-35, horizontal scaffold 2, with uniform mass m2=30.0 kg and length L2=2.00 m, hangs f

step 1 Let's write down our givens. We have M sub 1. This would be 50 kilograms. And this would be simp

In Fig. 12-35, horizontal scaffold 2, with uniform mass...

In Fig. $12-35,$ horizontal scaffold $2,$ with uniform mass $m_{2}=30.0$ $\mathrm{kg}$ and length $L_{2}=2.00 \mathrm{m},$ hangs from horizontal scaffold $1,$ with uniform mass $m_{1}=50.0 \mathrm{kg} . \mathrm{A} 20.0 \mathrm{kg}$ box of nails lies on scaffold 2, centered at distance $d=0.500 \mathrm{m}$ from the left end. What is the tension $T$ in the cable indicated?

In Fig. $12-35,$ horizontal scaffold $2,$ with uniform mass $m_{2}=30.0$
$\mathrm{kg}$ and length $L_{2}=2.00 \mathrm{m},$ hangs
from horizontal scaffold $1,$ with uniform mass $m_{1}=50.0 \mathrm{kg} . \mathrm{A} 20.0 \mathrm{kg}$
box of nails lies on scaffold 2, centered at distance $d=0.500 \mathrm{m}$ from the left end. What is the tension $T$ in
the cable indicated?

Key Concepts

Uniform Distribution of Mass

Uniform mass distribution means that the mass is evenly spread along the length of an object or beam. This concept simplifies calculations by allowing the center of mass to be easily identified, typically at the midpoint of the object. It is fundamental in problems involving beams or scaffolds, as it affects how gravitational forces contribute to both net forces and torques in the system.

Static Equilibrium

This concept involves objects or systems being at rest with no net force or torque acting on them. In the context of mechanics, all the forces (including gravitational and tension forces) and torques (moments due to these forces) must balance, ensuring that the system remains stable without acceleration or rotation.

Torque and Moments

Torque, also known as moment, is the tendency of a force to rotate an object about a pivot point. In static equilibrium problems, the sum of the clockwise torques must equal the sum of the counterclockwise torques. This principle is crucial when analyzing hanging beams or scaffolds, as it helps determine unknown forces such as tension in a supporting cable.

Center of Mass

The center of mass is the point at which the mass of a body or system is considered to be concentrated. For uniform objects, the center of mass is at the geometric center. When additional masses are added, such as a load placed asymmetrically, the location of the overall center of mass shifts. In equilibrium calculations, accurately determining this point is essential to correctly computing moments and analyzing the balance of forces.

Transcript

0:00 Let's write down our givens.

00:01 We have m sub 1.

00:03 This would be 50 kilograms.

00:06 And this would be simply the m sub 1 would simply be the horizontal scaffold number 1.

00:15 And then m sub 2 would be the lower scaffold, the scaffold mass.

00:20 This would be 30 kilograms.

00:23 This would be m, the mass of the package, 20 kilograms.

00:29 We know that then l sub 1 in this case rather l sub 2 this would simply be the lower scaffold length this is 2 .00 meters and then we know of course d is equaling 0 .5 0 meters and then we know that l sub 1 is going to be equal to l sub 2 plus 2 times d so this is simply equaling 2 plus 2 times 0 .5 so 3 .00 meters and we can say that we're going to use equation 129 and this would be applied at pivot at left and of lower scaffold and this would simply be essentially taking the moment about that pivot so negative m sub 2g multiplied by l sub 2 over 2 minus m m gd plus t sub r l sub 2.

01:57 We're in here, this is going to equal 0, and we're trying to find t sub r, where t sub r is the tension in the rope connecting the right end of the lower scaffold to the larger scaffold above it.

02:11 So essentially we can say that t subr would be equal to m sub 2g times l sub 2 over 2 plus and then this would all be divided by l sub 2.

02:31 And so we can solve.

02:35 This would be 30.

02:37 We'll lose the units because we have the units understood to the left.

02:43 So 30 times 9 .8 meters per second squared.

02:47 This would simply be the acceleration due to gravity...

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