3.15 Mass and Weight Tutorial

A 1-kilogram bag of nails weighs 9.81 N at the Earth's surface. What is the weight (in newtons) of 1 kilogram of butter at the Earth's surface?

9.8 N

True or False?

A 2-kilogram iron block has twice as much inertia as a 1 kilogram block of iron. *true* A 2-kilogram iron block has twice as much mass as a 1 kilogram block of iron. *true* A 2-kilogram iron block has twice as much volume as a 1 kilogram block of iron. *true* A 2-kilogram iron block has twice as much weight as a 1 kilogram block of iron. *true*

We are left with g = (Gme)/d2 (mo cancels out).

g = (Gme)/d2 The acceleration in a vacuum does not depend on the mass.

The mass of the space shuttle is about 5.06 E 5 kilograms. What would be the weight of the space shuttle as it sits on the launch pad? (q. 4)

m = 5.06 E 5 kg g = 9.81 m/s^2 W = mg W = (5.06 E 5 kg)(9.81 m/s^2) W = 4963860 N W = 5.0 E 6 N

If the mass of the Earth is 6.0 E 24 kilograms and its radius is 6.377 E 6 meters, use Newton's Law of Universal Gravitation to calculate the weight of the shuttle on the launch pad.

m1 = 6.0 E 24 kg m2 = 5.06 E 5 kg d = 6.377 E 6 m G = 6.67 E -11 (N* m^2)/kg^2 F = ? F = (Gm1m2)/d^2 = [(6.67 E -11 )(N m^2)/kg^2)( 6.0 E 24 kg)(5.06 E 5 kg)]/( 6.377 E 6 m)^2 F = 4979604 N F = 5.0 E 6 N

Assume that the shuttle is orbiting 3.22 E 5 meters above the surface of the Earth. Use Newton's Law of Universal Gravitation to calculate the weight of the shuttle as it orbits at this height. Hint: Remember that the "d" in the equation is the distance between the center of the shuttle and the center of the Earth.

m1 = 6.0 E 24 kg m2 = 5.06 E 5 kg d = 6.377 E 6 m G = 6.67 E -11 (N*m^2)/kg^2 F = ? F = (Gm1m2)/d^2 = [(6.67 E -11 )(N*m^2)/kg^2)( 6.0 E 24 kg)(5.06 E 5 kg)]/( 6.377 E 6 m + 3.22 E 5 m)^2 F = 4512401 N F = 4.5 E 6 N

Is the shuttle weightless while in orbit?

The shuttle is not weightless while in orbit. It retains over 90% of its Earth weight while in orbit.

Choose the best answer...

An apple that has a mass of 0.1 kilogram has the same mass wherever it is. The amount of matter that makes up the apple *does not depend upon* the location of the apple. It has the same resistance to acceleration wherever it is; its inertia everywhere is *the same*. The weight of the apple is a different story. It may weigh exactly 1 N in San Francisco and slightly less in mile-high Denver, Colorado. On the surface of the moon, the apple would weigh 1/6 N, and far out in outer space it may have almost no weight at all. The quantity that doesn't change with location is *mass*, and the quantity that may change with location is its *weight*. That's because *weight* is the force due to gravity on a body, and this force varies with distance. So weight is the force of gravity between two bodies, usually some small object in contact with the Earth. When we refer to the *weight* of an object, we are usually speaking of the gravitational force that attracts it to the Earth.

The weight of an object on Earth may be found by using this equation: Fg = Wo = (Gmome)/d^2

Fg = gravitational force = Wo = weight of the object G = 6.67 E -11 N*m2/kg2 mo = mass of the object me = mass of the Earth d^2 = the distance between the object and the Earth squared

General Overview (taken from Paul Hewitt's work):

Mass is often confused with weight. We say a heavy object contains a lot of matter. We often determine the amount of matter in an object by measuring its gravitational attraction to the Earth. However, mass is more fundamental than weight. Mass is a measure of the amount of a material in an object and depends only upon the number of and kind of atoms that compose it. Weight, on the other hand, is a measure of the gravitational force acting on the object. Weight depends upon the object's location. The amount of material in a particular stone is the same whether the stone is located on the Earth, on the moon, or in outer space. Hence, the stone's mass is the same in all of these locations. This could be determined by shaking the stone back and forth in these three locations. The same force would be required to shake the stone with the same rhythm whether the stone was on the Earth, on the moon, or in a force-free region of outer space. The stone's inertia, or mass, is solely a property of the stone and not its location. The weight of the stone would be very different on the Earth and on the moon, and still different in outer space. On the surface of the moon, the stone would have only one-sixth of the weight it has on the Earth. This is because the force of gravity on the moon is only one-sixth as strong as it is on the Earth. If the stone were in a relatively gravity-free region of space, its weight would be zero. Its mass, on the other hand, would not be zero. As you now know, mass is different from weight.

Mass

Mass is the quantity of matter in an object. More specifically, mass is a measure of the inertia, or "laziness," that an object exhibits in response to any effort made to start it, stop it, or otherwise change its state of motion. I remember once working with some other physics teachers to make the definition of "mass" more meaningful. We decided that mass could be defined as the amount of "stuff" in an object.

Units for measuring mass:

The SI unit of mass is the kilogram (kg). Some other units of mass are the gram, milligram, and slug.

Units for measuring weight:

The SI unit of weight is the newton (N). Some other units of weight are the dyne and pound.

Compare this answer (^) to question four.

The difference is 15744 N; when you put the numbers into significant digits, there is no difference.

Weight

The force of gravity on an object.

The relationship between mass and weight:

While mass and weight are not the same thing, they are proportional to each other in a given location. Objects with great mass have great weight; objects with little mass have little weight. In the same location, twice the mass weighs twice as much. Mass and weight are proportional to each other, but they are not equal to each other. Mass has to do with the amount of matter in the object, while weight has to do with how strongly that matter is attracted by gravity.

The equation relating mass and weight on Earth is Wo = mog.

Wo = weight of the object in newtons mo = mass of the object in kilograms g = acceleration due to gravity (9.81 m/s2 on Earth)