Why is inertial mass and gravitational mass

ACT Exam Prep. College Resources. AP Trivia. Sign in Sign up. AP Physics 1. Unit 3. Your typical high-school physics laboratory probably has an air track on which gliders will move almost without friction, which will do the trick. The easiest case is a head-on collision between two spherically symmetric objects. These objects move along a single line before and after the collision:.

In general, the collision will change the speeds of the spheres. We can use this fact to define the masses of the two objects, using the relation.

As soon as we have defined the unit of mass in other words, chosen one particular body as a standard , we can make experimental collisions and thus determine the masses of all other bodies. This definition is consistent with our everyday notion of larger and smaller masses or larger and smaller inertia, respectively.

The animation above shows an example: Before the collision, the cyan and ball and the violet one are moving towards each other equally fast, but in opposite directions.

However, the mass of the cyan ball is just a quarter that of the violet one. The mass we have defined in this way plays a key role in classical mechanics — that is, in the laws that describe how objects move under the influence of forces. The definition meshes with our everyday ideas of when forces are strong: pull more strongly, and the spring will be stretched further than by a weaker pull.

But the definition can do more than your subjective feeling of when a force is weaker and when it is stronger: It allows you to determine the ration of force strengths — we can measure when a force is two times, three times, four times as strong as another.

The shorthand version is. Gravity is special. Take two objects and let them fall, taking care to release them at the same time. If you release feather and lead weight at the same height, at the same time, they will stay next to each other as they fall:. This is known as the universality of free fall : Gravitational acceleration is the same for all objects. On cosmic scales, the situation is very similar. Consider smaller objects orbiting a central mass, the most important example being the planets of our Solar System orbiting the Sun.

The paths of free bodies define what we mean by "straight" and if we observe an object deviate from constant velocity, it must be because spacetime itself is curved. Formally, we state the equivalence principle this way: in any and every locally Lorentz inertial frame, the laws of special relativity must hold.

From this, we conclude that the only things which can define the geometric structure of spacetime are the paths of free bodies. Often, one finds references to the "strong" or "weak" equivalence principle. The weak equivalence principle has been stated, in the equality of gravitational and inertial mass and in the statement about special relativistic laws holding in every locally Lorentz frame, if we restrict that statement to the "laws of freely falling bodies.

Be, Al, Cu and Si test bodies using the Earth as attractor. Our null results consitute the most precise laboratory tests of the UFF. Our results showed that the proposed "fifth force" and its natural generalizations did not exist. Be, Al, Cu and Si test bodies attracted toward the Sun. The goal here was to complement the lunar laser-ranging data that, in effect, tests the UFF for the Earth and Moon falling toward the Sun. However, the laser-ranging test probes a combination of two effects, the differing gravitational self-energies and also the differing compositions the Earth has an Fe-Ni core while the moon does not of the Earth and Moon.

We are doing an experiment where we compare the accelerations toward the sun of special test bodies that have compositions very close to that of the Earth's core and to that of the Moon's surface.

We expect to do this well enough to take full advantage of the precision of the laser-ranging data. Be, Al, Cu and Si test bodies attracted toward the center of our Galaxy. In science there are facts and theories. The only facts are things we can measure, and then always with a measurement error. That the two masses are the same is a a theory.

A good theory as it has not been proven wrong, yet. But it could possibly be proven wrong with a different measurement. Nikolaj-K Nikolaj-K 7, 5 5 gold badges 34 34 silver badges 81 81 bronze badges. Krasnoholovets V. Krasnoholovets 9. Featured on Meta. Now live: A fully responsive profile. Linked 7. See more linked questions. Related Hot Network Questions. Question feed. Physics Stack Exchange works best with JavaScript enabled.

Accept all cookies Customize settings.