Mass & Weight

Question 1

Mass

Answer 1

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. 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.

Question 2

Weight

Answer 2

Weight, on the other hand, is a measure of the gravitational force acting on the object. Weight depends upon the object’s location. Weight of the stone is very different on the Earth and on the moon, and still different in outer space.

Question 3

Mass versus Weight Relationship

Answer 3

Proportional

Question 4

Mass and Weight Equation

Answer 4

W_o = m_og.

W<sub>o</sub> = weight of the object in newtons
m<sub>o</sub> = mass of the object in kilograms
g = acceleration due to gravity (9.81 m/s2 on Earth)

Question 5

Mass versus Weight Equations Relationship

Answer 5

F_g = W_o = (Gm_om_e)/d2

F_g = gravitational force = W_o = weight of the object

G = 6.67 E−11 N*m2/kg2

m_o = mass of the object

m_e = mass of the Earth

d² = the distance between the object and the Earth squared

We can combine these equations since they are both equal to weight (W):
m_og = (Gm_ome)/d²

We are left with g = (Gm_e)/d2 (m_o cancels out).

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

Question 6

True or False:

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

Answer 6

1. True
2. True
3. True
4. True
5. True

Question 7

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

(depends upon) (does not depend upon)

Question 8

The location of the apple. It has the same resistance to acceleration wherever it is; its inertia everywhere is
(the same) (different).

Question 9

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) (weight),

The quantity that may change with location is its
(mass) (weight).

That’s because
(mass) (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
(mass) (weight)
of an object, we are usually speaking of the gravitational force that attracts it to the Earth.

Answer 9

Mass

Weight

Weight

Weight

Question 10

The mass of the space shuttle is about 5.06 E5 kilograms. What would be the weight of the space shuttle as it sits on the launch pad? Be sure to show your work.

Answer 10

m = 5.06 E5 kg
g = 9.81 m/s2
W = mg
W = (5.06 E5 kg)(9.81 m/s2)
W = 4963860 N
W = 5.0 E6 N

Question 11

If the mass of the Earth is 6.0 E24 kilograms and its radius is 6.377 E6 meters, use Newton’s Law of Universal Gravitation to calculate the weight of the shuttle on the launch pad. Be sure to show your work.

Answer 11

m₁ = 6.0 E24 kg

m₂ = 5.06 E5 kg

d = 6.377 E6 m

G = 6.67 E−11 (N*m^₂)/kg²

F = ?

F = (Gm₁m₂)/d² = [(6.67 E−11 (N*m2)/kg2)(6.0 E24 kg)(5.06 E5 kg)]/(6.377 E6 m)²

F = 4979604 N

F = 5.0 E6 N

Question 12

How would you measure the mass of an object?

Answer 12

The inertial mass of a body determines its tendency to resist change in motion.

The gravitational mass determines its gravitational attraction for other masses.

In a laboratory setting, a common instrument would be a triple-beam balance.

Question 13

Define weight

Answer 13

Earth’s gravitation pull on a mass, the force by which a mass is attracted to the Earth. Weight is proportional to the body’s mass, the constant of proportionality being the gravitational field strength.

Question 14

How would you measure the weight of an object?

Answer 14

There are many ways to measure weight. A common method would be to use a spring scale.

Question 15

Newspapers often report that the astronauts in an orbiting space shuttle are “weightless.” In your own words, what is meant by the term “weightless”?

Answer 15

An apparent loss of weight experienced by a person in a situation in which they no longer feel the gravitation pull.

Question 16

The term “microgravity” is also used to describe the state of the astronauts in an orbiting shuttle. In your own words, what is meant by the term “microgravity”?

Answer 16

The prefix “micro” denotes E−6; the term “microgravity” would denote extremely small gravity.