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Show that the rate of change of your weight is$$-2 G \frac{m_{\mathrm{E}} m}{r^{3}} v$$if you are traveling directly away from Earth at constantspeed $v .$ Your mass is $m,$ and $r$ is your distance from thecenter of the Earth at any moment.

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$-2 G \frac{m_{e} m}{r^{3}} v$

Physics 101 Mechanics

Chapter 6

Gravitation and Newton's Synthesis

Physics Basics

Newton's Laws of Motion

Applying Newton's Laws

Gravitation

University of Washington

University of Sheffield

University of Winnipeg

Lectures

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.

03:55

In physics, orbital motion is the motion of an object around another object, which is often a star or planet. Orbital motion is affected by the gravity of the central object, as well as by the resistance of deep space (which is negligible at the distances of most orbits in the Solar System).

01:19

The gravitational attracti…

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(a) Show that the rate of …

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06:44

6.63. So we want to show that the rate at which our weight changes as we move away from the center of the earth at a constant speed is this So we want to find basically the time derivative of our weight under the assumption that we're moving away from the Earth. It Constance. So you know that your weight has just given by, uh, Newton's law of universal gravitation. So g m of the earth I am of you over our square. So now is a derivative of this. We get through the chain rule because it's going to be the rate at which your weight changes with respect to your distance from the center of the earth times the rate at which your distance from the centre of Earth changes with time. So this we're just going to get a negative, uh, two and an extra factor of our and the denominator here. So you get negative too. G m e m over our huge. Now that's this. And then the rt t is just given in the setup of the problem is your speed. And so now we've shown that this is true

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