4e. Mass and Weight [Beyond Books - Introduction to Physics Concepts]

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If an elephant and a feather were tossed from a building at the same time, which would hit the ground first?

Want to achieve an ideal weight? Try going to another planet, moon, or perhaps a neutron star.

The water spider's small mass enables it to walk on water despite not having huge feet. Humans, on the other hand, would need boat-sized feet to walk on water.

It may not be as momentous as the breakup of the Spice Girls, but scientists recently discovered that neutrinos have mass. Shout it from the rooftops!

4e. Mass and Weight

Cosmonauts train in a weightless environment provided by an airplane flying on a parabolic path.

Once again, mass and weight are not the same thing. True, these terms are used interchangeably in ordinary conversation, but physicists converse somewhat differently.

MASS is a fixed property of an object and does not depend on anything outside the object. It defines how much there is of the object and is related to its inertia.

WEIGHT, on the other hand, is the force required to support an object against the pull of gravity. A common illustration of this is when the same physics teacher who weighs 160 pounds on Earth weighs less on the Moon (same mass with less gravity equals less weight).

Mass is related to inertia.
Weight is related to both mass and gravity.

A person's weight on the Moon is 1/6 of his or her weight on Earth.
But how much mass and weight? Newton's second law explains how to measure mass: apply a force to an object, measure the object's acceleration, and then calculate the ratio

m = F

a

Once the mass is known, the weight can be calculated by using the expression weight = mg, where g is the acceleration of gravity (9.8 m/s²). Let's try some examples.

Example 1

What is the weight of a 25 kg child?
Because this triple-beam balance scale measures the mass (not the weight) of an object, it will read the same on any planet.

Example 2

What is the mass of a 1 N apple?

It may seem strange that the expression for weight has an acceleration in it, since objects are normally weighed at rest. Remember that the force of gravity acting on an object of mass "m" is given by F = mg, whether the object is moving or not. If the object happens to be in free fall (under the influence of gravity only), then Newton's second law says that F = ma. Comparing the two expressions for force, it is clear that a = g. Thus, the gravitational constant is the free-fall acceleration.

Weight a Minute

What if the mass of an object is unknown? Can its weight be measured? Sure — with a scale. Inside the scale is a spring that is stretched or compressed when a force acts on it. This distortion is indicated by a pointer attached to the spring. When a person stands on the scale, the tension in the spring mechanism matches his or her weight, and the pointer indicates this tension (the weight). Just remember that a scale measures weight, not mass.

Here's an example to illustrate.

What does this all mean, really? All of Newton's laws, including universal gravitation (which will be addressed later) relate force, acceleration, and mass. Weight, wherever and in whatever units it is measured, is a force that affects anything with mass. So the force really is with you!

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