5 a 0117 kg meterstick is supported at its 364 cm mark by a...

5. A 0.117 kg meterstick is supported at its 36.4 cm mark by a string attached to the ceiling. A 0.692 kg mass hangs vertically from the 4.73 cm mark. A mass is attached somewhere on the meterstick to keep it horizontal and in both rotational and translational equilibrium. The force applied by the string attaching the meter stick to the ceiling is 23.8 N. Find the value of the unknown mass. The acceleration of gravity is 9.81 m/s^2. Answer in units of kg. Find the point where the mass attaches to the stick

Transcript

00:01 Okay, we have a meter stick with a mass of 0 .106 kilograms supported at its 31 .6 centimeter mark by a string attached to the ceiling.

00:12 Here's our meter stick.

00:14 It's got a string at 31 centimeters pulling it up.

00:17 Call that force of tension t.

00:24 And then it has a .651 kilogram mass hanging from the 4 centimeter mark.

00:31 So close to the end here.

00:33 We're going to measure from this left end.

00:37 So increasing length to the right.

00:42 Call this one m1, and that force is going to be m1 times g.

00:48 I'm writing forces here.

00:55 Okay, let's see, yeah, okay.

01:02 And then we have an unknown mass somewhere along the meter stick.

01:09 Let's just put it over here.

01:11 Call it m2 times g.

01:14 Okay.

01:15 What other force do we have? the force of the meter stick, right? where does the weight of the meter stick act? so the weight can always draw it and say that it acts through the center of mass.

01:29 Call it, oh, i don't know, m sub s, first stick times g.

01:37 So where does this act? well, the meter stick's one meter long, right? so this is going to act at the 50 centimeter mark, right? because that's halfway along.

01:49 Okay.

01:50 So let's draw out some distances here.

01:55 So this first one, let's say that's a distance l1.

01:58 That's the 4 .07 centimeters.

02:02 This next one is, we'll call it l sub t.

02:06 And this is, it looks like it's this length, but what i want to represent is this total length.

02:16 So that's what that is.

02:18 L sub t is that full length.

02:20 And then we'll call this l sub s, that's the half meter, right? we're measuring from here.

02:28 Again, a little confusing.

02:30 And then this next one we'll call l2, again measured from the far left all the way out.

02:38 Okay, we're trying to find the value of the unknown mass, and then the point at which the mass attaches to the stick.

02:48 So, l2, essentially.

02:49 We're trying to find m2 and l2, that's what we're solving for.

02:53 Well, we're told this is that this ruler, or meter stick is in static equilibrium, right? it's not moving.

03:02 It's stable.

03:03 So the condition for static equilibrium is the sum of the forces of zero, and the sum of the moments, or however you'd like to write at torque, the sum of those is equal to zero.

03:20 So let's do the forces first and see what we get...

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