Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the...
Transcript of Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the...
![Page 1: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/1.jpg)
Momentum and Impulse
Conservation Laws
![Page 2: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/2.jpg)
Impulse
Fra
cket
on
ball
![Page 3: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/3.jpg)
ImpulseWhen the racket hits the ball
F(t)racket on ball = – F (t) ball on racket
Time interval from ti to tf is the same
Fr on b = mb (dvb/dt)
Fr on b dt = mb dvb
Define “Impulse”
€
J on ball = Fr on bdtti
t f
∫
![Page 4: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/4.jpg)
Momentum
Fr on b dt = mb dvb = d (mb vb)
Mass x Velocity = Momentum
pb = mb vb
Fr on b dt = d pb
€
J on ball = Fr on bdt = dpb
ti
tf
∫ti
t f
∫ = pf − pi
![Page 5: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/5.jpg)
Impulse Momentum
The impulse on an object in a time interval equals the object’s change of momentum.
![Page 6: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/6.jpg)
Average ForceMaximum Force
Fmax
The area under the triangle is the same as the area in part (a)
![Page 7: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/7.jpg)
![Page 8: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/8.jpg)
![Page 9: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/9.jpg)
![Page 10: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/10.jpg)
![Page 11: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/11.jpg)
Conservation of Momentum
![Page 12: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/12.jpg)
The momentum change of ball 1is equal and opposite to
the momentum change of ball 2
The total momentum isalways the same
![Page 13: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/13.jpg)
Inelastic Collisionv1
m1 m2before collision
after collision
v’
stuck together
Use conservation of momentum to find v’
![Page 14: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/14.jpg)
Inelastic Collision1-D
before
€
ptotal = m1v1
after
€
′ p total = (m1 + m2 ) ′ v =
€
m1v1 = (m1 + m2 ) ′ v
€
′ v =m1
(m1 + m2 )v1
![Page 15: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/15.jpg)
Inelastic Collisionequal masses
€
′ v =m1
(m1 + m2 )v1
€
m1 = m2
€
′ v =m1
(2m1)v1 =
v1
2
![Page 16: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/16.jpg)
Inelastic Collisionm2 =2 m1
v’=?
![Page 17: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/17.jpg)
![Page 18: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/18.jpg)
Explosions
v′2
m1 m2before “explosion”
v′1
after “explosion”ptotal = 0
p′total = 0
€
m1 ′ v 1 + m2 ′ v 2 = 0
€
′ v 1′ v 2
=m2
m1
Inverse Relationship
![Page 19: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/19.jpg)
Reverse Explosionv2before v1
after m1 m2
p′total = 0
ptotal = 0
€
′ v 1′ v 2
=m2
m1
Velcro
Note that if you sit on one of the blocks, the “explosion” looks like a collision:
Change of reference frame.
![Page 20: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/20.jpg)
Explosions in 2-D
Find v3 and θ
![Page 21: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/21.jpg)
unknowns
Explosions in 2-D
€
pix = p1x + p2x + p3x
€
piy = p1y + p2 y + p3 y = 0
![Page 22: Momentum and Impulse - SFU.caImpulse Momentum The impulse on an object in a time interval equals the object’s change of momentum. Average Force Maximum Force F max The area under](https://reader036.fdocuments.net/reader036/viewer/2022071218/604f465c6e1ab80b6070402f/html5/thumbnails/22.jpg)
€
p3 y = −( p1y + p2 y )
€
p3x = pix − ( p1x + p2x )
€
pix = MVix = (10g)(2.0m/s) = 20 g•m/s
€
p2x = (3g)(−10.0m/s)
= −30 g•m/s
€
p1x = (3g)(12.0m/s) cos 40°
= 27.6 g•ms
0
€
p1y = (3g)(12.0m/s) sin 40¡
= 23.1 g•m/s
= 22.4 g•m/s
= –23.1 g•m/s
Accountancy 101
Find θ and v3.