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As your bus rounds a flat curve at constant speed, a package with mass $0.500 \mathrm{kg},$ suspended from the luggage compartment of the bus by a string 45.0 $\mathrm{cm}$ long, is found to hang at rest relative to the bus, with the string making an angle of $30.0^{\circ}$ with the vertical. In this position, the package is 50.0 $\mathrm{m}$ from the center of curvature of the curve. What isthe speed of the bus?

16.8 m/s

Physics 101 Mechanics

Chapter 6

Circular Motion and Gravitatio

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

University of Washington

Simon Fraser University

University of Winnipeg

Lectures

04:34

In physics, kinematics is the description of the motion of objects and systems in the frame of reference defined by the observer. An observer has to be specified, otherwise the term is meaningless.

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

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You are riding in a school…

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As your bus rounds a flat …

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01:26

Okay, President 55 is tricky. So you have this bus which I'm drawing as a tangle. Here, let's pretend those wheels and, um, on this on the ceiling of this busters, as attached by a string and because the bus is turning, there's gonna be an angle in the mess, so I'll just read this angle. Nice Stella. Um, we know there's a single data here as well, so it's just dry. This massive red. Make it more colorful. Um, let's see. We were given a lot of information and problem. That's the tricky part is we don't actually need all this information. Um, for example, the length of the string in the mass of the mass. We won't even used them now, since the mass is leaning towards left here, it means that the bus is currently turning right, and since it's turning, it's making a circle, and the radius of a circle is 50 meters. Are the buses 50 meters from the center of curvature of the curve is doing and yes, but we should always ask ourselves first is what do we want? This problem Well, here we want the speeder. What's the speed of the bus as inferred from this angle here in the mass. Okay, well, as always, but physics problem, we can start with free body diagram. So let's think about all the forces here. One of the movie gravity and another one will be the tension Joe Culp T and the attention forces air into doors to rope because the rope is pulling on the mess. Also draw her access x and y always helpful. Okay, so we don't really know what the speed is. Well, that's what you want to know. Um, on one way to get access to the speed is with the exploration, because this is sent a circular motion. Exploration is Reese Cordoba are. And in X, you have some of the forces is on the key, but it will be the projection of tea and the ex access T T sign theta. And we know this is a close to M times exploration, or sometimes escort are because our exploration exes towards the center of this circle. Great. So we have the speed. Um, we do have the mass on DDE have the radius of the struggles. Well, but we don't have to, So we're gonna look in a way as well. And why, If they're some of the forces must banks out. So we have the sum of the forces here. Or, in other words, gravitational forces. The gravitational force is equal to projection of tea along the Y axis. That would be t co sign Andi F G is simply empty, right? So from this, we can isolate tea, and we know thus that t equals n g over co sign. And here we could, huh? Could find that t equals. And these quote over our signed it from this equation. Now, if we put those two equation together, which we get and I will write this on your tab is that and b squared over r I want to thread. This is blue. Come on and B squared over. R um, sign Peter, which is what I could hear. Is it quantity? But he's also go to m g over co Santa great. The masses consult and we can isolate the speed from this s so that would be these squared equals g r signed their over co sign patera or V equals the square root of G R and then sign over co sign. That's it. 10. Great. We have all we need now. So as you can see the masses and appear, the length of the stream doesn't appear. Um, anything we need is the angle and the regis of purity energy. But we always know what is G. He is 9.8 meters per second squared and our 50 meters while tango is 30 degrees great and we're pretty much done. Just crunch those numbers down and we get final speed for the bust of 16.8 meters per second.

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