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A satellite moves on a circular earth orbit that has a radius of $6.7 \times 10^{6} \mathrm{~m} .$ A model airplane is flying on a $15-\mathrm{m}$ guideline in a horizontal circle. The guideline is parallel to the ground. Find the speed of the plane such that the plane and the satellite have the same centripetal acceleration.

12$m / s$

Physics 101 Mechanics

Chapter 5

Dynamics of Uniform Circular Motion

Newton's Laws of Motion

Applying Newton's Laws

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Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

03:43

In physics, dynamics is the branch of physics concerned with the study of forces and their effect on matter, commonly in the context of motion. In everyday usage, "dynamics" usually refers to a set of laws that describe the motion of bodies under the action of a system of forces. The motion of a body is described by its position and its velocity as the time value varies. The science of dynamics can be subdivided into, Dynamics of a rigid body, which deals with the motion of a rigid body in the frame of reference where it is considered to be a rigid body. Dynamics of a continuum, which deals with the motion of a continuous system, in the frame of reference where the system is considered to be a continuum.

02:45

A satellite moves on a cir…

02:23

A satellite moves in a cir…

06:34

(a) Find the radius of the…

04:24

A satellite orbits the Ear…

03:57

An Earth Satellite An Ear…

02:35

A satellite is in a circul…

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01:55

01:23

02:48

The speed of a satellite l…

02:52

Find the orbital speed of …

here, we have to find, um, a relationship between the velocities of a paper plane and a satellite such that they have these same centripetal acceleration. Now, initially, it might seem like we're not given enough information since we I don't know the velocity of the plane or the velocity of the satellite, but we have a way to solve for that second quantity. We know that for a satellite, the centripetal force is always equal to the gravitational force. That's what causes the object to move in a circle in the first place. That means that we can set up inequality and B squared is equal to M is the mass of the earth times g over our square. This are over here, actually isn't square to return my equation role. But from there, we can simplify to write an equation for V V has to be equal to the mass of the earth times G over the radius. And now we have an equation for the velocity of the satellite, all in terms of known values. So now we can get a round to actually writing our ratio that'll let assault. Now we know that the, um equation for angular acceleration is equal to these squared. But for our that means that yes, squared over R s must be equal to the peace. Weird over r p Now we just found the equation for Yes, Let's rearrange his to sell for VP. That's how me, equal to the square root a V a squared over rs times RP. And now we could also plug in for um are me s so then that that isn't all of this is going to be equal to we re right up here The square root of the mass of the earth have the gravitational constant over our radius for satellite times the square root of or P over or this And once again, that's equal to the velocity of our plane. And now all that's left to do is plug in our quantities. I'm gonna leave out the mass of the earth and the gravitational continent because they're pretty long numbers that you confined in your textbook. But we know a radius of our satellite. It's 6.7 times 10 to the sixth meters times the square root of our plane, which 15 meters over that same quantity, and we find that the velocity of our plane is equal to 12 meters per second

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