Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Physics I 95.141 LECTURE 16...
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Transcript of Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Physics I 95.141 LECTURE 16...
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Physics I95.141
LECTURE 1611/03/10
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Outline• Impulse• Conservation of Momentum and Energy• Elastic and Inelastic Collisions
• What do we know?– Units– Kinematic equations– Freely falling objects– Vectors– Kinematics + Vectors = Vector
Kinematics– Relative motion– Projectile motion– Uniform circular motion– Newton’s Laws– Force of Gravity/Normal Force– Free Body Diagrams– Problem solving
– Uniform Circular Motion– Newton’s Law of Universal Gravitation – Weightlessness– Laws– Work by Constant Force– Scalar Product of Vectors– Work done by varying Force– Work-Energy Theorem– Conservative, non-conservative Forces– Potential Energy– Mechanical Energy – Conservation of Energy– Dissipative Forces– Gravitational Potential Revisited– Power– Momentum and Force– Conservation of Momentum– Collisions– Impulse
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Collisions and Impulse
• Over the course of a collision, the inter-object Forces change very quickly.
• Example: a serve in tennis…..– We can think of this as a spring system, with the
compression/extension of the ball/strings occurring over a small fraction of a second (~5ms)
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Collision and Impulse
• From Newton’s second law, we can write:
• This integral is known as the Impulse
dt
pdFnet
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Collisions and Impulse
• The impulse of a Force is simply the integral of that Force over the time the Force acts.
pppdtFJ if
t
t
f
i
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Example• Imagine the force exerted by a tennis racket
on the ball during a serve can be approximated by the F vs time plot below. What is the impulse acting on the .056 kg ball? What is the speed of the serve?
)(msTime10
For
ce (
kN)
2
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Bond, James Bond• Using Energy, can we explain why the window doesn’t
break when they push off, but does when they come back to it?
ovh
fv
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Bond, James Bond• Using Impulse, can we why the window breaks?
– Assume the push-off takes 0.5 seconds, so that Bond goes from 0m/s to vo in 0.5s.
– On the return, however, Bond and Wai Lin brace their legs, and they are slowed to a stop in 0.05 seconds.
ovfv
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Bond, James Bond
• Calculate average Force for each case (push-off and impact)
ovfv
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Conservation of Momentum
• In the previous lecture we discussed the quantity of momentum
• The change of momentum of an object can be related to the net Force on the object
• In a collision, momentum is conserved, as long as no external forces act on the system
• Impulse
vmp
amdt
systemsystem pp
pdtFJt
t
2
1
Department of Physics and Applied Physics95.141, F2010, Lecture 16
What about Energy?• In the case of the fender bender where the cars lock bumpers and
travel on together, is kinetic energy conserved?• Remember, Car1 (1000kg) traveling at 10m/s hits Car2 (1000kg),
which is at rest, and their bumpers lock together.
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Conservation of Energy• Total energy is always conserved.• In collisions, sometimes we can say that not only is
total energy conserved, but kinetic energy is conserved.– During a collision, for a split second, some or all energy is
stored in elastic potential energy.– But this energy is quickly returned to either thermal or kinetic
energy (or both) – Two hard elastic objects (billiard balls) usually end up with
the same total kinetic energy
• When this happens, the collision is referred to as an elastic collision.
Department of Physics and Applied Physics95.141, F2010, Lecture 16
1D Elastic Collisions
• We must now consider both conservation of energy and momentum.
• In the last section, we had to give the masses and 3 out of 4 velocities.
• If we know the collision is elastic, then we only need to know 2 out 4 of the velocities.
Department of Physics and Applied Physics95.141, F2010, Lecture 16
1D Elastic Collisions Example• Ball 1 is traveling with a velocity of 10 m/s and Ball 2 with a velocity
of 3 m/s. What are the final velocities of the balls, if they have the same mass?
10m/s 3m/s
Department of Physics and Applied Physics95.141, F2010, Lecture 16
In General• Say you have two masses (mA and mB), each traveling
with initial speeds (vA and vB).
BBAABBAA vmvmvmvm 2222
2
1
2
1
2
1
2
1BBABBA vmvmvmvm
AA
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Interesting….
• For any elastic collision in 1D, the relative speed of the two objects after the collision is the same as it was before the collision, but the direction opposite!
• This is a simpler way of writing conservation of Energy for 1D!
ABBABA vvvvvv
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Elastic Collision, Equal Masses
• If you start with two mass (mA = mB).
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Unequal Masses, Target at Rest• If you start with two mass (mA and mB) with mB at rest.
• What happens if mA is much more massive than the target?
• What if target is much more massive (mA << mB)
BA
AAB mm
mvv
2
BA
BAAA mm
mmvv
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Newton’s Cradle
• Given what you now know about elastic collisions, you should be able to explain this:
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Inelastic Collisions
• A collision where Kinetic Energy is not conserved is known as an inelastic collision.
• Technically, all collisions are inelastic, since there is always some energy that is converted to heat, even when we model these collisions as elastic.
• A collision/process is inelastic when…– Some of the mechanical energy is converted into
thermal or potential energy or…– In the case of explosions, when potential energy
(chemical or nuclear, for example) is converted into kinetic energy
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Newton’s Cradle, revisited
• Suppose the period of motion for this Newton’s cradle is 0.5 s, and the height the 100g ball swings to decreases by 1mm each swing. How much thermal energy is generated each period? What is the power is dissipated?
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Perfectly Inelastic Collisions
• If two object stick together after a collision, this is known as a perfectly inelastic collision.
• Let’s revisit our car crash again.– 1000kg car, travelling 10m/s hits a car at rest and
their bumpers lock (perfectly inelastic collision)
Department of Physics and Applied Physics95.141, F2010, Lecture 16
What is the final speed of the dead guy?
• mbullet=20g• vbullet=405m/s• mbadguy=70kg
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Ballistic Pendulum
• A device used to measure the speed of a projectile.
vo v1
hmM M+m
Department of Physics and Applied Physics95.141, F2010, Lecture 16
Ballistic Pendulum
• If the projectile mass is 10g and the pendulum mass is 3kg, and the pendulum swings to a height of 5cm, what is the velocity of the projectile before the collision?