Which is more likely to knock it over (larger impulse) A The stone ball B The clay ball C It won t matter

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Lucy Morgan
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1 Collisions in 2d &

2 Craig wants to knock over a stone pillar by throwing a ball at it. He has two balls of identical mass, which he can throw with the same speed. A stone ball which will collide perfectly elastically A clay ball which will collide perfectly inelastically (i.e. it will stick to the surface when it hits) Which is more likely to knock it over (larger impulse) A The stone ball B The clay ball C It won t matter

3 What is conserved? A W mech B p cat C p sys, x D W mech & p sys, x E neither is conserved

4 Elastic Collisions in 1d given unknown v Ai v Bi v Af v Bf m A m B m A m B m A m B momentum: energy: p i = m A v Ai + m B v Bi = m A v Af + m B v Bf = p f K i = 0.5 m A v Ai m B v Bi 2 = 0.5 m A v Af m B v Bf2 = K f 2 equations for 2 unknowns

5 Elastic Collisions in 2d given v Ai v Af unknown v Bi v Bf Q: can we find the final velocities from conservation laws alone in 2d (as we could in 1d)? A Yes B No C I don t understand the question

6 Elastic Collisions in 2d given v Ai v Af unknown v Bi 4 v Bf equations: unknowns: v Axf, v Ayf, v Bxf, v Byf 3 p xi = m A v Axi + m B v Bxi = m A v Axf + m B v Bxf = p xf p yi = m A v Ayi + m B v Byi = m A v Ayf + m B v Byf = p yf Not enough information K i = 0.5 m A v Ai m B v Bi 2 = 0.5 m A v Af m B v Bf 2 = K f

7 Elastic Collisions in 2d given v Ai important v Af v Bi 4 v Bf equations: unknowns: v Axf, v Ayf, v Bxf, v Byf p xi = m A v Axi + m B v Bxi = m A v Axf + m B v Bxf = p xf 3 p yi = m A v Ayi + m B v Byi = m A v Ayf + m B v Byf = p yf K i = 0.5 m A v Ai m B v Bi 2 = 0.5 m A v Af m B v Bf = K f

8 Elastic Collisions in 2d given v Ai important v Af v Bf v Bi 4 equations: unknowns: v Axf, v Ayf, v Bxf, v Byf p xi = m A v Axi + m B v Bxi = m A v Axf + m B v Bxf = p xf 3 p yi = m A v Ayi + m B v Byi = m A v Ayf + m B v Byf = p yf K i = 0.5 m A v Ai m B v Bi 2 = 0.5 m A v Af m B v Bf = K f

9 Cue ball is 6 m/s at the stationary 8-ball. The cue ball deflects to 60 o. How fast is each ball moving after the collision? A equal speeds B Cue ball moves faster C 8-ball moves faster D not enough information v Ai = 6 m/s v Bi =0 60 o 30 o v Af v Bf

10 Cue ball is 6 m/s at the stationary 8-ball. The cue ball deflects to 60 o. How fast is each ball moving after the collision? p fx = [ v Af cos(60 o ) + v Bf cos(30 o ) ]m A = 6 m A p fy = [ v Af sin(60 o ) - v Bf sin(30 o ) ]m A = 0 v Af = v Bf sin(30 o )/sin(60 o ) = 0.58 v Bf v Ai = 6 m/s v Bi =0 p i = m A 6ˆ i 60 o 30 o v Af v Bf

11 Cue ball is 6 m/s at the stationary 8-ball. The cue ball deflects to 60 o. How fast is each ball moving after the collision? p fx = [ v Af cos(60 o ) + v Bf cos(30 o ) ]m A = 6 m A p fy = [ v Af sin(60 o ) - v Bf sin(30 o ) ]m A = 0 C 8-ball moves faster v Af = v Bf sin(30 o )/sin(60 o ) = 0.58 v Bf 0.5 v Af v Bf = 6 v Ai = 6 m/s v Bi =0 p i = m A 6ˆ i 1 m v 2 2 A Af + 1 m v 2 2 B Bf = 1.15 v Bf = 6 v Bf = 5.2 m/s v Af = 3 m/s Q: Does this conserve energy? 60 o 30 o = 1 m [ 2 A (3)2 + (5.2) 2 ] = 1 m 2 A (6) v Af v Bf

12 Rotation

13 Reading Question The units of angular acceleration α are A m/s 2 B dimensionless C rad (radians) D rad/s 2

14 30 o Rotation A ladder is leaning against a wall, as shown, when a sudden gust of wind knocks it over. It pivots about its end and takes 1.5 sec to go from the wall to the ground. What is its average angular velocity? A rad/sec B rad/sec C rad/sec D rad/sec

15 30 o Rotation A ladder is leaning against a wall, as shown, when a sudden gust of wind knocks it over. It pivots about its end and takes 1.5 sec to go from the wall to the ground. What is its average angular velocity? θ i = 120 o = 2π/3 = 2.1 θ f = 0 A rad/sec B rad/sec C rad/sec D rad/sec Δθ = θ f - θ i = -2.1 rad

16 50 cm A 50 cm potters wheel spins down at a constant angular acceleration α = 0.5 rad/s 2 from an initial ang. vel. of ω ο = rad/sec. How much time does it take to come to rest? A B C D E which equation would you use?

17 50 cm A 50 cm potters wheel spins down at a constant angular acceleration α = 0.5 rad/s 2 from an initial ang. vel. of ω ο = rad/sec. How much time does it take to come to rest? A B C D E which equation would you use? ω i = -16 ω f = 0 t = -(ω f - ω i )/α = 32 sec

18 50 cm A 50 cm potters wheel spins down at a constant angular acceleration α = 0.5 rad/s 2 from an initial ang. vel. of ω ο = rad/sec. How many rotations will it undergo? ω i = -16 ω f = 0 t = 32 sec A 512 B 256 C 81 D 41

19 50 cm A 50 cm potters wheel spins down at a constant angular acceleration α = 0.5 rad/s 2 from an initial ang. vel. of ω ο = rad/sec. How many rotations will it undergo? ω i = -16 ω f = 0 t = 32 sec A 512 B 256 C 81 D 41 0 = (-16) 2 + 2(0.5)( θ - θ o ) θ - θ o = -256 rad (θ - θ o )/2π =

20 25 cm A 50 cm potters wheel spins down at a constant angular acceleration α = 0.5 rad/s 2 from an initial ang. vel. of ω ο = rad/sec. A lump of clay sits at a point 25 cm from the center. What is the linear speed of the clay at t=8 sec? ω i = -16 A 12 m/s B 6 m/s C 4 m/s D 3 m/s E 1.5 m/s

21 25 cm A 50 cm potters wheel spins down at a constant angular acceleration α = 0.5 rad/s 2 from an initial ang. vel. of ω ο = rad/sec. A lump of clay sits at a point 25 cm from the center. What is the linear speed of the clay at t=8 sec? ω i = -16 ω = (8) = -12 rad/s A 12 m/s B 6 m/s C 4 m/s D 3 m/s E 1.5 m/s v = ω r = -12 (0.25) = 3 m/s

22 25 cm A 50 cm potters wheel spins down at a constant angular acceleration α = 0.5 rad/s 2 from an initial ang. vel. of ω ο = rad/sec. A lump of clay sits at a point 25 cm from ω = -1 rad/s the center. Which could be the v = 0.25 m/s acceleration of the clay at 30 sec? B A C D E

23 25 cm A 50 cm potters wheel spins down at a constant angular acceleration α = 0.5 rad/s 2 from an initial ang. vel. of ω ο = rad/sec. A lump of clay sits at a point 25 cm from ω = -1 rad/s the center. Which could be the v = 0.25 m/s acceleration of the clay at 30 sec? a c = v2 r = (!r)2 r a c = 0.25 m/s 2 a t =!r =! 2 r B A a t = m/s 2! a =! a t +! a c C D E

24 Rotation L=4 m 8 m/s A 4m ladder (m=10 kg) is leaning against a wall, as shown, when a sudden gust of wind knocks it over. At the instant it hits the ground the ladder s tip is moving at 8 m/s. What is the ladder s angular velocity at that time? A -2 rad/s B -0.5 rad/s C +0.5 rad/s D +2 rad/s

25 Rotation L=4 m 8 m/s A 4m ladder (m=10 kg) is leaning against a wall, as shown, when a sudden gust of wind knocks it over. At the instant it hits the ground the ladder s tip is moving at 8 m/s. What is the kinetic energy of the ladder?

Welcome back to Physics 211

Welcome back to Physics 211 Today s agenda: Impulse and momentum 09-2 1 Current assignments Reading: Chapter 10 in textbook Prelecture due next Tuesday HW#8 due this Friday at 5 pm. 09-2 2 9-2.1 A crash