ONE DIMENSIONAL MOTION ACCELERATION IN THE Y DIRECTION NOTES.
2 Dimensional Motion Notes
-
Upload
athena-huynh -
Category
Documents
-
view
215 -
download
0
Transcript of 2 Dimensional Motion Notes
7/28/2019 2 Dimensional Motion Notes
http://slidepdf.com/reader/full/2-dimensional-motion-notes 1/5
Chapter 7: Motion in 2 Dimensions
When an object is projected so that it moves horizontally as well as vertically, it is said to be a 2-
D projectile.
When we solve such problems, we use the same equations of motion to do calculations in the
horizontal and vertical directions independently.
Note: horizontally, ; vertically,
Horizontally Launched Projectile
Example 1: A cannonball fired horizontally on the top of a 75 m high cliff moves with an initial
speed of 1769 ft/s (note: 1 ft = 0.3048 m).
a) Determine how long it takes for the cannonball to drop into the sea.
b) Determine the horizontal displacement, d x .
c) Determine the final velocity of the cannonball just before hitting the water.
Solution:
a) Vertically <y>
7/28/2019 2 Dimensional Motion Notes
http://slidepdf.com/reader/full/2-dimensional-motion-notes 2/5
b) Horizontally <x>
c) Vertically <y>
√
( ) The final velocity, , is , below the horizontal.
Circular Motion
To change an object’s velocity, we need to apply a non-zero net force ( ). When an
object moves in a curve, the direction of the object constantly changes and so its velocity is
changing (even if its speed remains constant). Thus a force is needed to make an object move in
a curved motion.
In circular motion, the acceleration of an object moving with constant speed, v, with a radius of curvature, r, is given by:
where ac is the centripetal acceleration.
θ
V
7/28/2019 2 Dimensional Motion Notes
http://slidepdf.com/reader/full/2-dimensional-motion-notes 3/5
The net force for uniform circular motion is . F c and ac are always directed towards the
centre of the motion.
Example: The Earth revolves around the sun in about 365 days in a year. Calculate the
centripetal force acting on the Earth if we assume uniform circular motion.
Data:
mass of Earth = 5.98 × 1024 kg
radius of Earth’s orbit around the Sun = 1.50 × 1011 m
This centripetal force on the Earth is caused by the gravitational pull of the Sun on the Earth.
Forces in 2-D: Inclined Plane
At the point of moving,
and
(on a level surface)
Moving at a constant
speed,
Find by drawing a graph of or against or :
7/28/2019 2 Dimensional Motion Notes
http://slidepdf.com/reader/full/2-dimensional-motion-notes 4/5
Now find on an inclined plane:
Case A: Frictionless
Case B: Not Frictionless
At the point of moving, :
SOH
CAH
TOA
8 data points
7/28/2019 2 Dimensional Motion Notes
http://slidepdf.com/reader/full/2-dimensional-motion-notes 5/5
Example
Calculate the acceleration down the slope when
a) the ramp is frictionless
b) the ramp has a coefficient of friction (kinetic) of 0.05 with the object’s base surface