Why are denser objects heavier? Density is defined as: \(D = \frac {M}{V}\) where M is mass and V is volume and mass is defined as the quantity of matter contained in an object \(\int \rho dV\) where p is the density. What I don't understand is why a denser object is heavier than a less dense object when the mass is the same?
In Kidsgeo it's written that as air is heated it expands becoming less dense, and as a result, lighter. Because it is lighter, it rises upwards above the cooler air. http://www.kidsgeo.com/geography-for-kids/0070-adiabatic-temperature-changes.php
That's correct. I think you're misunderstanding density, somehow. Heated air takes up a larger volume - it's less heavy per unit of volume than cold air. But the still the same weight.
But when we say heavy we mean weight and weight is \(w = mg\). So did you mean heavier or more massive?
What's the difference between weight and mass, as you understand it? Something is heavy because it has mass. The more mass the more weight...
Pluto, the total weight and the total mass before and after heating are the same, what changed is only the density. Example: Initial mass, m[sub]1[/sub] = 1 gr.......(which means, initial weight, w[sub]1[/sub] = m[sub]1[/sub].g = 10 gr.m/s[sup]2[/sup]) Initial volume, v[sub]1[/sub] = 1 L Initial density, d[sub]1[/sub]= m[sub]1[/sub]/v[sub]1[/sub] = 1 gr/L after heating: Final mass, m[sub]2[/sub] = 1 gr.......(which means, final weight, w[sub]2[/sub] = m[sub]2[/sub].g = 10 gr.m/s[sup]2[/sup] = w[sub]1[/sub]) Final volume, v[sub]2[/sub] = 10 L Final density, d[sub]2[/sub] = m[sub]2[/sub]/v[sub]2[/sub] = 0.1 gr/L = 0.1 d[sub]1[/sub] (and hence is less dense).
Right. Wrong. The mass - and therefore, the weight - stays the same. It's neither heavier nor lighter. Wrong. It rises because it is less dense than the air around it. It's the Archimedean Principle you've probably heard about in connection with water: An object immersed in water experiences an upwards force equal to the weight of the displaced water. If the object weighs more than the water it displaces, it sinks. If it weighs less than the water it displaces, it floats. This applies no matter what medium you're immersing the object in. Here, you're "immersing" hot air in cool air. Since the hot air weighs less than cool air of equal volume, it rises. But the weight of the air you heated stays the same.
The authors of that website either arrived at a correct explanation by sheer dumb luck or by knowing what they were talking about but talking about it would be a useless distraction at a web site targeted at kids. There are multiple, conflicting definitions of the meaning of the word "weight". The negative responses you have received so far are using weight to mean mass times the acceleration due to gravity. This is the nice, simple definition of weight taught in lower level physics classes and some (but not all) college level physics classes. There are a couple of problems with this definition. It is immeasurable. No device can be constructed to measure the acceleration (or force) due to gravity. It is a synonym for gravitational force. So why not call it gravitational force rather than weight? An alternate definition (wikipedia calls it "apparent weight"; others call it "weight") is the net sum of all real forces acting on a body except for gravity. Alternatively, that which is measured by an ideal scale (spring scale). With this definition in mind, imagine weighing yourself on a typical bathroom scale. Now grab a bunch of balloons inflated with helium and weigh yourself again. The measured weight will have decreased even though the mass of the human+balloon system is greater than your mass alone. The balloons have negative (apparent) weight. Buoyancy is a real force and thus is a part of the apparent weight of an object.
Pluto2, when they eventually get around to building a base on the Moon or Mars, go up there and try running around a sharp 90 degree corner. You'll find that you crash into the wall. Mass is the same regardless of gravity, although your weight changes in a weaker gravitational field (100 kg Earth/16 kg the Moon, or 37 kg on Mars). So if you move around carelessly, without regard for the fact that your mass doesn't alter, you're going to end up rather bruised.:wallbang:
I think you are confusing with pressure. Two objects that have the same amount of mass will weight the same, size does not matter.
No. It depends on what you mean by weight. Size does matter if you are using the definition of weight used in general relativity (what an ideal spring scale measures) or the definition of weight used in other more advanced physics (the sum of all forces except for gravity). Those two definitions are very similar. If you use either of those definitions, size does matter.
For example, consider inflating a balloon. In ordinary conditions, an inflated balloon is lighter than an uninflated balloon, but has more mass.
So, to directly answer the O.P... Because they are less buoyant. They have less volume, so they displace less of the surrounding medium, so (some detailed steps skipped) the surrounding medium doesn't push upward on them as much. If there is no surrounding medium (i.e. in a vaccuum), then denser objects are not heavier.
Several of you have been assuming weight is mass times gravitational acceleration. That certainly is one meaning of the term: weight is a synonym for gravitational force. This is the meaning of the term taught in elementary physics classes. There are several other meanings. Colloquially and legally, weight is a synonym for mass. Yet a third meaning is used when we say astronauts aboard the space station are weightless. In this sense, weight (typically called apparent weight), is the sum of all real forces acting on an object except for gravitational force. Consider a healthy Los Angeleno. One fine summer day he steps on a spring scale and finds his weight (apparent weight sense) to be 174.6 lbf. After a few calculations he determines his actual weight to be 175.3 lbf. That 0.7 lbf difference between his apparent weight and actual weight arises from centrifugal force (0.5 lbf) and buoyancy (0.2 lbf). His legal weight at Los Angeles: 175 lbm. The next day he climbs to the top of Mt McKinley. There, his apparent weight is 174.6 lbf while his actual weight is 175.2 lbf. That 0.6 lbf difference between is apparent weight and actual weight once again arises from centrifugal force and buoyancy, but at altitude he is displacing considerably less air. (He is also closer to the Earth's rotation axis because even though McKinley is 14,025 feet higher than LA, the difference in latitude overwhelms the altitude difference.) His legal weight at the top of Mt. McKinley: 175 lbm. A while later he is inducted into the astronaut corp and flies up the the ISS. There his apparent weight is nearly zero. His actual weight: 156.7 lbf. His legal weight on the ISS: 175 lbm.
Consider two balls 100 kg in mass each. One is 1 inch in diameter and the other is 100 inches in diameter. Place them on a weight scale (on Earth) with accuracy to infinite decimal places. The ball that is 1 inch in diameter will actually weight more according to the gravity equation. Why? The variable r = distance from the center of Earth to the center of a ball. This r is greater for the less dense object than the more dense object. But this difference is so minute that we just say that they weight the same.
