An object is falling and it weighs 25 kg (on a scale, presumably). What is its mass?
I know that weight is measured in Newtons and mass in kilograms, but what if a problem states that something weighs in kilograms? Would I still use $\text w=mg$?
[Physics] If something weighs 25 kg, how to find the mass of the object
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Related Solutions
The mass of the object always stays the same. The balance can only measure the downward force exerted on it by the bob. The force measured by the balance is simply the weight of the masses on one side needed to balance the downward force of the bob on the other side.
In air, the only appreciable force will be the downward force from gravity, aka the weight of the bob. In water, there is also a significant upward force due to the buoyant force exerted on the bob by the water. So in the water, the balance is measuring the difference between the weight of the bob and the buoyant force. The relevant physics and formulas can all be found on Wikipedia easily. If you define the (true) specific gravity $S$ as the ratio of the density of your bob $\rho_B$ to the density of water, i.e. $S = \frac{\rho_B}{\rho_{H_20}}$, you should be able to show that $$ \frac{f_{water}}{f_{air}} = 1 - \frac{1}{S},$$ where $f_{air}$ and $f_{water}$ are the forces measured by your balance in air and in water respectively.
Regarding the use of grams or Newtons, they are often used interchangeably to talk about the weight of an object, although this is technically rather sloppy because they are not the same thing in general. The two units measure fundamentally different things, one is a mass and one is a force. However, since all objects on the Earth are subject to the same acceleration $g$ due to gravity, there is a natural way to change between one and the other, by the formula $f = mg$. Whenever people use grams to measure forces, or Newtons to measure mass, it is this correspondence that they are implicitly referring to.
[Physics] If nothing weighs something then doesn’t that mean there is mass associated with spacetime
OK, I watched the video.
It consists of two parts. The first part talks about General relativity and the introduction of a cosmological constant, which from the argument should not exist in completely empty space.
He then goes to the Quantum Field Theory vacuum which has the continuous creation and annihilation of all possible fields of virtual particles all the time, and illustrates it with the proton. His discourse assumes that the proton is made up of three quarks and the rest is empty space. The theory I know does not say so, it says the rest is a gluon to quark antiquark and back sea, that holds everything together to form the proton. It is not empty space because energy exists within the proton, it is not zero.
So the presentation is incomplete and seems to me misleading, if we are to project the inside energy momentum conditions of a proton to cosmological scales and the cosmological constant. They are not the same.
Anyway the argument he seems to be leading to is incomplete.
If mass is associated with spacetime then wouldn't it be the mass associated with spacetime which waves in a double slit experiment?
In the double slit experiments, mass does not wave. The elementary particles are point particles as far as our experiments have explored, when they appear as particles, the appear at a specific (x,y,z,t). What "waves" is the probability of finding that particle at a specific (x,y,z,t) which probability is calculated by squaring the quantum mechanical amplitude describing the "particle/wave" entity which probability shows interference patterns in collective observations at double slit experiments.
In my opinion, until we have a solid theory which quantizes gravity and includes the standard model of particle physics speculation about how fields appear in cosmological terms is not productive. We have to wait for a theory, and a string theory seems to be the only candidate that can do this , to examine the cosmological constant of classical general relativity.
Best Answer
I've seen some books use kg for kgf (kilogram-force), even though they shouldn't have conflated them.
But in this case it's not too harmful: if 25 kg means mass, as it should, then it the answer is direct. On the other hand, if 25 kg really means 25 kilogram-force, then the answer is the same under the assumption of standard gravity, because $1\,\text{kgf}$ is by definition $(1\,\text{kg})(9.80665\,\text{m/s}^2)$, the weight of 1 kg under 1 standard gravity.