Werner Ens
518 Allen
Office Hours: Monday 2 - 6 pm(or by appointment)
Werner Ens
518 Allen
Office Hours: Monday 2 - 6 pm(or by appointment)
My PowerPoint lecture notes available on-line
www.physics.umanitoba.ca/~ens/16.102lectures.html
(Complete lecture notes prepared last year by Professor Birchall are available at the course web site)
Quiz1. Which arrows correctly represent
acceleration?
(a) (b) (c) (d) (e)
Quiz2. Which is the trajectory after the line is cut?
(a)
(b)
(c)
(d)
Quiz3. What happens to an astronaut if his tether to
an orbiting space station is cut?
(a) Stays with space station
(b) Falls behind in orbit
(c) Falls to earth
(d) Lost in space (moves away)
(e) Remains stationary with respect to the sun
Quiz4. What happens if an astronaut releases a ball
while standing on the moon?
(a) It falls to the ground (moon)
(b) It rises
(c) It stays where it is released
(d) Moves horizontally (moon’s horizon)
Quiz solutions1. Which arrows correctly represent
acceleration?
(a) (b) (c) (d) (e)
Quiz solutions2. Which is the trajectory after the line is cut?
(a)
(b)
(c)
(d)
Quiz solutions3. What happens to an astronaut if his tether to
an orbiting space station is cut?
(a) Stays with space station
(b) Falls behind in orbit
(c) Falls to earth
(d) Lost in space (moves away)
(e) Remains stationary with respect to the sun
Quiz solutions4. What happens if an astronaut releases a ball
while standing on the moon?
(a) It stays where it is
(b) It rises
(c) It falls to the ground (moon)
(d) Moves horizontally (moon’s horizon)
Quiz solutions
1 d, 2 b, 3 a, 4 c
Chapter 1
Introduction
Mathematical Concepts
1) Representation of physical quantities
• Arithmetic is abstract: 10 - 5 = 5• A physical quantity (distance) requires
comparison to a standard: L = 10 is meaningless
m
10 m
• A physical quantity is an algebraic product of a number and a unit: L = 10 m
2) Units combine algebraically; Dimensional Analysis
€
d3 = d1 + d2
d1 = 5m;
d2 = 8m
€
d3 = 5m + 8m
= (5 + 8)m
=13m
2) Units combine algebraically; Dimensional Analysis
€
A = l • w
l = 8m
w = 4m
€
A = 8m• 4m = 32m2
€
V = lwh ≠ 32h
V = 32m2h
If h = 2m, then V = 64m3
Example: Vector Addition• Jogger runs 145 m 20.0º East of North
– Displacement vector A
• Then 105 m 35.0º South of East– Displacement vector B
• Find resultant displacement C=A+B
A =145 m; θA =70º
θA
20º
x (E)
y (N) rA
35º rB
rC
θC
θB
B =105 m; θB =360º−35º
→ 325º or −35º
Find C and θC
Step 0: Draw a picture & organize data
Example: Vector Addition
A =145 m; θA =70ºθA20º
x (E)
y (N) rA
• Step 1: Convert to component representation
Ax =AcosθA =(145m)cos70º=49.6m
Ax
Ay
Ay =AsinθA =(145m) sin70º=136m
Example: Vector Addition
x (E)
y (N) 35º rB
θB
B =105 m; θB =360º−35º
→ 325º or −35º
• Step 1: Convert to component representation
Ax =AcosθA =(145m)cos70º=49.6mAy =AsinθA =(145m) sin70º=136m
By
Bx
By =BsinθB =(105m) sin(-35º) =−60.2mBx =BcosθB =(105m) cos(-35º) =86.0m
Example: Vector Addition• Step 2: Sum components
Ax =49.6mAy =136m
By =−60.2mBx =86.0mθA
20º
x (E)
y (N) rA
35º rB
rC
θC
θB
Cx =Ax + Bx =135.6m
Cy =Ay + By =76.0m
Example: Vector Addition• Step 3: Convert result to geometric representation
(magnitude, direction)
Ax =49.6mAy =136m
By =−60.2mBx =86.0m
x (E)
y (N)
rC
θC
Cx =135.6m
Cy =76.0m
C = Cx2 +Cy
2 =155m
Cx
Cy
tanθc =Cy
Cx
=.560 → θC = 29.2º (North of East)
Example: Vector Addition• Step 3: Convert to geometric representation (magnitude, direction)
x (E)
y (N)
rC
θC
Cx =135.6m
Cy =−76.0m
C = Cx2 +Cy
2 =155m
Cx
Cy
tanθc =Cy
Cx
=−.560 → θC = −29.2º
Example: Vector Addition• Step 3: Convert to geometric representation (magnitude, direction)
x (E)
y (N)
rC
θC Cx =−135.6m
Cy =−76.0m
C = Cx2 +Cy
2 =155m
Cx
Cy
tanθc =Cy
Cx
=.560 → θC = 29.2º?
→ θC = 29.2º +180º = 209.2º