Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Phys141: Chapter 4 - Projectile Motion and Circular Motion - Prof. Wolfgang Losert, Study notes of Physics

University of MarylandPhysics
Prof. Wolfgang Losert

Chapter 4 of phys141, focusing on projectile motion and circular motion. Topics include parabolic trajectories, maximum height calculations, the relationship between horizontal velocity and distance, and the components of acceleration in 2d. Students are encouraged to read chapter 5.1-4, complete an online quiz, and prepare for lab 2.

Typology: Study notes

Pre 2010

Uploaded on 02/13/2009

koofers-user-ugi
koofers-user-ugi 🇺🇸

4.5

(1)

10 documents

1 / 4

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
1
Phys141 – Fri 9/15
•Today: End of Chapter 4
Administrative:
Midterm 1: Oct 4
•Material up to Chapter 7
•Mix of conceptual questions and quantitative questions
•Only material covered in class or HW or lab
•Similar to HW and quizzes and examples given in lecture
ToDo
•Read: Chapter 5.1-4
•online quiz,
•prepare lab2
Example of 2D motion:
Projectile motion
•Example: Projectile motion
–Interactive Figure 4.11
• Assumptions:
– Gravitational acceleration gconstant over
the range of motion
– Air friction is negligible
Chapter 4
Projectile motion has
Parabolic Trajectory
Separate into horizontal (x) and vertical (y) motion
y(t) = yi+ vyi t-½gt2(y axis points UPWARD -> gravitational accel.
is negative)
x (t) = xi+ vxi t (no horizontal acceleration)
Initial conditions
vxi = vicos
θ
xi=0
vyi = visin
θ
yi=0
-> x(t) = (vicos
θ
)t
y(t) = (visin
θ
) t-½gt2
Combining the equations gives y(x):
()
2
22
tan 2cos
i
ii
g
yx x
v
θθ
⎛⎞
=−
⎜⎟
⎝⎠
Both y(t) and y(x) are quadratic functions -> parabola
Chapter 4
pf3
pf4

Partial preview of the text

Download Phys141: Chapter 4 - Projectile Motion and Circular Motion - Prof. Wolfgang Losert and more Study notes Physics in PDF only on Docsity!

Phys141 – Fri 9/

  • Today: End of Chapter 4

Administrative: Midterm 1: Oct 4

  • Material up to Chapter 7
  • Mix of conceptual questions and quantitative questions
  • Only material covered in class or HW or lab
  • Similar to HW and quizzes and examples given in lecture

ToDo

  • Read: Chapter 5.1-
  • online quiz,
  • prepare lab

Example of 2D motion:

Projectile motion

  • Example: Projectile motion
    • Interactive Figure 4.
  • Assumptions:
    • Gravitational acceleration g constant over the range of motion
    • Air friction is negligible

Chapter 4

Projectile motion has

Parabolic Trajectory

Separate into horizontal (x) and vertical (y) motion y(t) = y i + v yi t - ½ g t^2 (y axis points UPWARD -> gravitational accel. is negative) x (t) = x i + v xi t (no horizontal acceleration) Initial conditions v xi = v i cos θ x i = v yi = v i sin θ y i = -> x(t) = ( vi cos θ) t y(t) = ( vi sin θ) t - ½ gt^2 Combining the equations gives y(x): ( tan^ ) 2 2 2 i (^2) i cos i y x g x v

θ θ

⎛ ⎞ = − ⎜ ⎟ ⎝ ⎠

Both y(t) and y(x) are quadratic functions -> parabola

Chapter 4

Height of a Projectile, equation

The maximum height of the projectile can be

found in terms of the initial velocity vector:

Note: Maximum height means

(1) Change in y with x is zero:

(2) AND: Change in y with time is zero:

Use (1) or (2) to calculate maximum y (assuming the starting point as y=0): (^2) sin 2 2

h v^ i^ i g

θ

dy 0 dx = d yd t = 0

More About the Range of a Projectile

AF4.

Chapter 4

•Vertical initial velocity determines how long the object is in the air

•Horizontal initial velocity determines how far the object gets in that time -> To maximize horizontal distance, there is a tradeoff between maximizing horizontal speed or the time spent in the air

Acceleration in 2D

  • Acceleration: Change in velocity vector - Magnitude of the velocity vector may change - The direction of the velocity vector may change

d

dt

v

a

Chapter 4

Total Acceleration, equations

  • The tangential acceleration:
  • The radial acceleration:
  • The total acceleration:
    • Magnitude

t

d a dt

v

2 r C

v a a r

2 2

a = a r + at

Total Acceleration, In Terms of

Unit Vectors

  • Define the following unit vectors - r lies along the radius vector − θ is tangent to the circle
  • The total acceleration is

r ˆ and θ^ ˆ

2 ˆ (^) ˆ t r

d v dt r

= + = θ−

v a a a r

Chapter 4