# 5.4 Mass and weight  (Page 3/5)

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Check Your Understanding For [link] , find the acceleration when the farmer’s applied force is 230.0 N.

$a=2.78\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}$

Can you avoid the boulder field and land safely just before your fuel runs out, as Neil Armstrong did in 1969? This version of the classic video game accurately simulates the real motion of the lunar lander, with the correct mass, thrust, fuel consumption rate, and lunar gravity. The real lunar lander is hard to control.

Use this interactive simulation to move the Sun, Earth, Moon, and space station to see the effects on their gravitational forces and orbital paths. Visualize the sizes and distances between different heavenly bodies, and turn off gravity to see what would happen without it.

## Summary

• Mass is the quantity of matter in a substance.
• The weight of an object is the net force on a falling object, or its gravitational force. The object experiences acceleration due to gravity.
• Some upward resistance force from the air acts on all falling objects on Earth, so they can never truly be in free fall.
• Careful distinctions must be made between free fall and weightlessness using the definition of weight as force due to gravity acting on an object of a certain mass.

## Conceptual questions

What is the relationship between weight and mass? Which is an intrinsic, unchanging property of a body?

How much does a 70-kg astronaut weight in space, far from any celestial body? What is her mass at this location?

The astronaut is truly weightless in the location described, because there is no large body (planet or star) nearby to exert a gravitational force. Her mass is 70 kg regardless of where she is located.

Which of the following statements is accurate?

(a) Mass and weight are the same thing expressed in different units.

(b) If an object has no weight, it must have no mass.

(c) If the weight of an object varies, so must the mass.

(d) Mass and inertia are different concepts.

(e) Weight is always proportional to mass.

When you stand on Earth, your feet push against it with a force equal to your weight. Why doesn’t Earth accelerate away from you?

The force you exert (a contact force equal in magnitude to your weight) is small. Earth is extremely massive by comparison. Thus, the acceleration of Earth would be incredibly small. To see this, use Newton’s second law to calculate the acceleration you would cause if your weight is 600.0 N and the mass of Earth is $6.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{24}\phantom{\rule{0.2em}{0ex}}\text{kg}$ .

How would you give the value of $\stackrel{\to }{g}$ in vector form?

## Problems

The weight of an astronaut plus his space suit on the Moon is only 250 N. (a) How much does the suited astronaut weigh on Earth? (b) What is the mass on the Moon? On Earth?

a. $\begin{array}{ccc}\hfill {w}_{\text{Moon}}& =\hfill & m{g}_{\text{Moon}}\hfill \\ \hfill m& =\hfill & 150\phantom{\rule{0.2em}{0ex}}\text{kg}\hfill \\ \hfill {w}_{\text{Earth}}& =\hfill & 1.5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{N}\hfill \end{array}$ ; b. Mass does not change, so the suited astronaut’s mass on both Earth and the Moon is $150\phantom{\rule{0.2em}{0ex}}\text{kg.}$

Suppose the mass of a fully loaded module in which astronauts take off from the Moon is $1.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}$ kg. The thrust of its engines is $3.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}$ N. (a) Calculate the module’s magnitude of acceleration in a vertical takeoff from the Moon. (b) Could it lift off from Earth? If not, why not? If it could, calculate the magnitude of its acceleration.

A rocket sled accelerates at a rate of ${49.0\phantom{\rule{0.2em}{0ex}}\text{m/s}}^{2}$ . Its passenger has a mass of 75.0 kg. (a) Calculate the horizontal component of the force the seat exerts against his body. Compare this with his weight using a ratio. (b) Calculate the direction and magnitude of the total force the seat exerts against his body.

a. $\begin{array}{ccc}\hfill {F}_{\text{h}}& =\hfill & 3.68\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{N and}\hfill \\ \hfill w& =\hfill & 7.35\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{2}\phantom{\rule{0.2em}{0ex}}\text{N}\hfill \\ \hfill \frac{{F}_{\text{h}}}{w}& =\hfill & 5.00\phantom{\rule{0.2em}{0ex}}\text{times greater than weight}\hfill \end{array}$ ;
b. $\begin{array}{ccc}\hfill {F}_{\text{net}}& =\hfill & 3750\phantom{\rule{0.2em}{0ex}}\text{N}\hfill \\ \hfill \theta & =\hfill & 11.3\text{°}\phantom{\rule{0.2em}{0ex}}\text{from horizontal}\hfill \end{array}$

Repeat the previous problem for a situation in which the rocket sled decelerates at a rate of ${201\phantom{\rule{0.2em}{0ex}}\text{m/s}}^{2}$ . In this problem, the forces are exerted by the seat and the seat belt.

A body of mass 2.00 kg is pushed straight upward by a 25.0 N vertical force. What is its acceleration?

$\begin{array}{ccc}\hfill w& =\hfill & 19.6\phantom{\rule{0.2em}{0ex}}\text{N}\hfill \\ \hfill {F}_{\text{net}}& =\hfill & 5.40\phantom{\rule{0.2em}{0ex}}\text{N}\hfill \\ \hfill {F}_{\text{net}}& =\hfill & ma⇒a=2.70\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}\hfill \end{array}$

A car weighing 12,500 N starts from rest and accelerates to 83.0 km/h in 5.00 s. The friction force is 1350 N. Find the applied force produced by the engine.

A body with a mass of 10.0 kg is assumed to be in Earth’s gravitational field with $g=9.80\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}$ . What is its acceleration?

$0.60\stackrel{^}{i}-8.4\stackrel{^}{j}\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}$

A fireman has mass m ; he hears the fire alarm and slides down the pole with acceleration a (which is less than g in magnitude). (a) Write an equation giving the vertical force he must apply to the pole. (b) If his mass is 90.0 kg and he accelerates at $5.00\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2},$ what is the magnitude of his applied force?

A baseball catcher is performing a stunt for a television commercial. He will catch a baseball (mass 145 g) dropped from a height of 60.0 m above his glove. His glove stops the ball in 0.0100 s. What is the force exerted by his glove on the ball?

497 N

When the Moon is directly overhead at sunset, the force by Earth on the Moon, ${F}_{\text{EM}}$ , is essentially at $90\text{°}$ to the force by the Sun on the Moon, ${F}_{\text{SM}}$ , as shown below. Given that ${F}_{\text{EM}}=1.98\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{20}\phantom{\rule{0.2em}{0ex}}\text{N}$ and ${F}_{\text{SM}}=4.36\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{20}\phantom{\rule{0.2em}{0ex}}\text{N},$ all other forces on the Moon are negligible, and the mass of the Moon is $7.35\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{22}\phantom{\rule{0.2em}{0ex}}\text{kg},$ determine the magnitude of the Moon’s acceleration.

#### Questions & Answers

can i get application of projectile motion?
when firing a cannon
morteza
Ok i got a question I'm not asking how gravity works. I would like to know why gravity works. like why is gravity the way it is. What is the true nature of gravity?
gravity pulls towards a mass...like every object is pulled towards earth
Ashok
One answer for that is exchange particles. Those particlescreate a field and if there is a field e.g. electromagnetic there is also force. same should go for gravitational field where exchange particle is called graviton and it creates gravitational field, which acts on everything that has mass.
Resid
@Ashok no that's how gravity works not why it works
Daniel
An automobile traveling with an initial velocity of 25m/s is accelerated to 35m/s in 6s,the wheel of the automobile is 80cm in diameter. find * The angular acceleration
what is the formula for pressure?
force/area
Kidus
force is newtom
Kidus
and area is meter squared
Kidus
so in SI units pressure is N/m^2
Kidus
In customary United States units pressure is lb/in^2. pound per square inch
Kidus
who is Newton?
scientist
Jeevan
a scientist
Peter
that discovered law of motion
Peter
ok
John
but who is Isaac newton?
John
a postmodernist would say that he did not discover them, he made them up and they're not actually a reality in itself, but a mere construct by which we decided to observe the word around us
elo
how?
Qhoshe
Besides his work on universal gravitation (gravity), Newton developed the 3 laws of motion which form the basic principles of modern physics. His discovery of calculus led the way to more powerful methods of solving mathematical problems. His work in optics included the study of white light and
Daniel
and the color spectrum
Daniel
what is a scalar quantity
scalar: are quantity have numerical value
muslim
is that a better way in defining scalar quantity
Peter
thanks
muslim
quantity that has magnitude but no direction
Peter
upward force and downward force lift
upward force and downward force on lift
hi
Etini
hi
elo
hy
Xander
Hello
Jux_dob
hi
Peter
Helo
Tobi
Yes what about it?
Daniel
what's the answer? I can't get it
what is the question again?
Sallieu
What's this conversation?
Zareen
what is catenation? and give examples
sununu
How many kilometres in 1 mile
Nessy
1.609km in 1mile
Faqir
what's the si unit of impulse
The Newton second (N•s)
Ethan
what is the s. I unit of current
Amphere(A)
imam
thanks man
Roland
u r welcome
imam
the velocity of a boat related to water is 3i+4j and that of water related to earth is i-3j. what is the velocity of the boat relative to earth.If unit vector i and j represent 1km/hour east and north respectively
what is head to tail rule?
Explain Head to tail rule?
kinza
what is the guess theorem
viva question and answer on practical youngs modulus by streching
send me vvi que
rupesh
a car can cover a distance of 522km on 36 Liter's of petrol, how far can it travel on 14 liter of petrol.
Isaac
yoo the ans is 193
Joseph
whats a two dimensional force
what are two dimensional force?