# 2.7 Falling objects

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• Describe the effects of gravity on objects in motion.
• Describe the motion of objects that are in free fall.
• Calculate the position and velocity of objects in free fall.

Falling objects form an interesting class of motion problems. For example, we can estimate the depth of a vertical mine shaft by dropping a rock into it and listening for the rock to hit the bottom. By applying the kinematics developed so far to falling objects, we can examine some interesting situations and learn much about gravity in the process.

## Gravity

The most remarkable and unexpected fact about falling objects is that, if air resistance and friction are negligible, then in a given location all objects fall toward the center of Earth with the same constant acceleration , independent of their mass . This experimentally determined fact is unexpected, because we are so accustomed to the effects of air resistance and friction that we expect light objects to fall slower than heavy ones.

In the real world, air resistance can cause a lighter object to fall slower than a heavier object of the same size. A tennis ball will reach the ground after a hard baseball dropped at the same time. (It might be difficult to observe the difference if the height is not large.) Air resistance opposes the motion of an object through the air, while friction between objects—such as between clothes and a laundry chute or between a stone and a pool into which it is dropped—also opposes motion between them. For the ideal situations of these first few chapters, an object falling without air resistance or friction is defined to be in free-fall    .

The force of gravity causes objects to fall toward the center of Earth. The acceleration of free-falling objects is therefore called the acceleration due to gravity    . The acceleration due to gravity is constant , which means we can apply the kinematics equations to any falling object where air resistance and friction are negligible. This opens a broad class of interesting situations to us. The acceleration due to gravity is so important that its magnitude is given its own symbol, $g$ . It is constant at any given location on Earth and has the average value

$g=9\text{.}{\text{80 m/s}}^{2}\text{.}$

Although $g$ varies from $9\text{.}{\text{78 m/s}}^{2}$ to  $9\text{.}{\text{83 m/s}}^{2}$ , depending on latitude, altitude, underlying geological formations, and local topography, the average value of $9\text{.}{\text{80 m/s}}^{2}$ will be used in this text unless otherwise specified. The direction of the acceleration due to gravity is downward (towards the center of Earth) . In fact, its direction defines what we call vertical. Note that whether the acceleration $a$ in the kinematic equations has the value $+g$ or $-g$ depends on how we define our coordinate system. If we define the upward direction as positive, then $a=-g=-9\text{.}{\text{80 m/s}}^{2}$ , and if we define the downward direction as positive, then $a=g=9\text{.}{\text{80 m/s}}^{2}$ .

#### Questions & Answers

What is conductivity
It is the ease with which electrical charges or heat can be transmitted through a material or a solution.
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how to find magnitude and direction
how to caclculate for speed
Arjune
derivation of ohms law
derivation of resistance
Kazeem
R=v/I where R=resistor, v=voltage, I=current
Kazeem
magnitude
Arjune
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
Arjune
Electric current is the flow of electrons
is there really flow of electrons exist?
babar
Yes It exists
Cffrrcvccgg
explain plz how electrons flow
babar
if electron flows from where first come and end the first one
babar
an electron will flow accross a conductor because or when it posseses kinectic energy
Cffrrcvccgg
electron can not flow jist trasmit electrical energy
ghulam
free electrons of conductor
ankita
electric means the flow heat current.
electric means the flow of heat current in a circuit.
Serah
What is electric
electric means?
ghulam
electric means the flow of heat current in a circuit.
Serah
a boy cycles continuously through a distance of 1.0km in 5minutes. calculate his average speed in ms-1(meter per second). how do I solve this
speed = distance/time be sure to convert the km to m and minutes to seconds check my utube video "mathwithmrv speed"
PhysicswithMrV
d=1.0km÷1000=0.001 t=5×60=300s s=d\t s=0.001/300=0.0000033m\s
Serah
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
Arjune
why we cannot use DC instead of AC in a transformer
becuse the d .c cannot travel for long distance trnsmission
ghulam
what is physics
branch of science which deals with matter energy and their relationship between them
ghulam
Life science
the
what is heat and temperature
how does sound affect temperature
sound is directly proportional to the temperature.
juny
how to solve wave question
I would like to know how I am not at all smart when it comes to math. please explain so I can understand. sincerly
Emma
Just know d relationship btw 1)wave length 2)frequency and velocity
Talhatu
First of all, you are smart and you will get it👍🏽... v = f × wavelength see my youtube channel: "mathwithmrv" if you want to know how to rearrange equations using the balance method
PhysicswithMrV
nice self promotion though xD
Beatrax
thanks dear
Chuks
hi pls help me with this question A ball is projected vertically upwards from the top of a tower 60m high with a velocity of 30ms1.what is the maximum height above the ground level?how long does it take to reach the ground level?
mahmoud
please guys help, what is the difference between concave lens and convex lens
convex lens brings rays of light to a focus while concave diverges rays of light
Christian
for mmHg to kPa yes
Matthew
it depends on the size
please what is concave lens
Vincent
a lens which diverge the ray of light
rinzuala
concave diverges light
Matthew
thank you guys
Vincent
A diverging lens
Yusuf
What is isotope
Yusuf
each of two or more forms of the same element that contain equal numbers of protons but different numbers of neutrons in their nuclei, and hence differ in relative atomic mass but not in chemical properties; in particular, a radioactive form of an element. "some elements have only one stable isotope
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what is wire wound resistors?