# Apparent weight and true weight

I want to know what do we actually measure in a weight machine, true weight or apparent weight? Please help me in understanding this concept.

• Weight is the force that earth exerts on a body. The force is proportional to its mass. So, if you are not accelerating in the frame of earth, the weight measured by the machine is the true weight. – Apoorv Potnis May 17 '17 at 7:58
• – Kunal Pawar May 17 '17 at 8:04
• Possible duplicate of How can a beam balance measure mass? – Yashas May 17 '17 at 14:50
• I don't understand the reason for closure. It's pretty clear what's being asked: What's the difference between apparent weight and true weight, and which of the two do "weighing machines" measure? The supposed duplicate? It asks about balance beams, and the sole answer is incorrect. Balance beams measure mass. The terms apparent weight and true weight are used in multiple questions and answers, but we have not yet had a question that asks the simple question being asked here. – David Hammen May 17 '17 at 21:27
• Voting to reopen. – David Hammen May 17 '17 at 21:27

A weighing machine measures the force exerted by a body on the weighing machine.
Newton's third law then predicts that there is a force of the same magnitude and opposite in direction acting on the body producing the force.

On the Earth if the weighing machine and the body are not accelerating (ignoring the rotation of the Earth) then the reading on the weighing machine will be the weight of the body.

If the weighing machine and the body are accelerating then you could call the reading on the weighing machine the apparent weight of the body.
So including the effect of the rotation of the Earth it is only at the geographic poles that reading on the weighing machine is the weight of the body.
Elsewhere on the Earth the reading on the weighing machine will be lower than at the poles so you could call that the apparent weight.
The difference between these readings is small.

If the weight of the body is $10 \, \rm N$ then with the weighing machine and the body in a stationary lift, or a lift moving at constant velocity upwards or downwards the reading on the weighing machine would be $10 \, \rm N$ which is the weight of the body.

If the weighting machine and the lift had an upward acceleration of $5 \,\rm m s^{-2}$ then the reading on the weighing machine would be $15 \, \rm N$ and you could say that the apparent weight of the body was $15 \, \rm N$

If the weighting machine and the lift had a downward acceleration of $5 \,\rm m s^{-2}$ then the reading on the weighing machine would be $5 \, \rm N$ and you could say that the apparent weight of the body was $5 \, \rm N$

If the weighting machine and the lift had a downward acceleration of $10 \,\rm m s^{-2}$ then the reading on the weighing machine would be $0 \, \rm N$ and you could say that the apparent weight of the body was zero - the body appeared to be weightless.

The definition of weight that I have used is that the weight of a body is the force on the body due to the gravitational attraction of the Earth.

However others define the weight of a body as the reading on a weighing machine as explained by Walter Lewin in one of his 8.01 Classical Mechanics lectures.
Using this definition a body is weightless when it is in free fall.

I want to know what do we actually measure in a weight machine, true weight or apparent weight?

What a "weighing machine" measures depends on the nature of the machine. A spring scale measures the compression of a spring that balances out the forces and torques exerted by the object on the spring pan. Assuming no torque, the force exerted by the test object on the pan is the downward normal force. The force exerted by the pan on the test object is the equal-but-opposite upward normal force. This is test object's apparent weight (ignoring buoyancy). The compression of the spring is thus an analog for apparent weight. Assuming a Hookean spring, this compression can readily be converted to apparent weight. There are a number of other types of devices that effectively measure apparent weight.

A balance scale measures the ratio of the apparent weight of a test object versus that of an object with a known mass. Since apparent weight is proportional to mass, a balance scale measures the test object's mass. A spring scale on the Moon will register about 1/6 of the value the scale would on the Earth for a given test object. A balance scale on the Moon will register more or less the same as that on the Earth for a given test object, "more or less" because the reduced gravity will increase the measurement error. A spring scale in the Space Station will register zero, more or less. A balance scale won't work in the Space Station because 0/0 is indeterminate.

What about true weight? A spring scale on a zero-g airplane flight will register a weight ranging between zero and twice the object's typical weight. The variation in the object's true weight will be very small; true weight decreases by about 0.0003086 m/s2 per kilometer of altitude above sea level. A spring scale measures apparent weight rather than true weight.

There's a difference between apparent weight and true weight, even for an object at rest on the surface of the Earth. The Earth's rotation means that an object on the surface of the Earth undergoes a constant magnitude acceleration toward the Earth's rotation axis of about $R_E\cos\phi$ from the Earth's rotation axis, where $R_E$ is the Earth's radius and $\phi$ is latitude. This acceleration means that true weight of an object at rest on the surface of the Earth exceeds the object's apparent weight by about $m R_E\Omega^2\cos\phi$, where $m$ is the object's mass and $\Omega$ is the Earth's sidereal rotation rate.

I want to know what do we actually measure in a weight machine, true weight or apparent weight? Please help me in understanding this concept.

In physics we do not have true and apparent weight.

We have weight and mass.

Weight is a force. It's the mass times the gravitational acceleration (or any acceleration the body feels).

Mass is very difficult to provide a strict definition for in physics.

The simplest way to think of it is that, although your weight varies depending on the acceleration you experience, your mass (in everyday Newtonian physics) does not - it's a constant.

We can also relate mass to momentum, something we cannot generally do with weight (because we'd have to allow for different forces). It turns out that we can also relate mass to energy using relativity and that opens up some very important physics. We could not do the same thing with weight because weight varies depending on force.

Note that if I'm not experiencing any force I have no weight - like in free fall. But I still have mass and I can still have momentum and because momentum is linked to mass, I can describe momentum with mass but not with weight.

An example, how do I relate the weight of a planet with it's gravitational field ? Well first of all, how do I even define it's weight ? I can't do that in a consistent way, but I can use it's mass to work out it's gravitational field.