Department of Physics and Applied Physics 95.141, S2010, Lecture 15 Physics I 95.141 LECTURE 15...
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Department of Physics and Applied Physics95.141, S2010, Lecture 15
Physics I95.141
LECTURE 1510/27/10
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Video Example
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Video Example• How much Thermal Energy is generated in
reentry?• What is the average power generated in
reentry?
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300
620,7
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6Earth
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Department of Physics and Applied Physics95.141, S2010, Lecture 15
Energy Conservation
• Initial Mechanical Energy before re-entry:
• Mechanical Energy after re-entry:
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Solve for Energies
• Change in Potential Energy
• Change in Kinetic Energy
• Change in Thermal Energy
• Power
r
mGMrU E)(
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Exam Prep Problem• A 2kg mass is placed on a spring with spring constant k (k=5,000,000). The
system is placed on the surface of the moon. In this problem we want to determine how much the spring must be compressed in order for the mass to escape the gravitational potential of the moon.
• A) (5pts) Write the expression for the gravitational potential of the mass at the surface of the moon.
• B) (5pts) Determine the gravitational potential of the mass once it has escaped the moon’s pull.
• C) (7pts) What must the velocity of the object be once it leaves the spring in order for the mass to escape the moon’s pull?
• D) (8pts) How far must the spring be compressed in order for the mass to escape the moon’s pull?
kgMkmR moonmoon223 1035.7,1074.1
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Exam Prep Problem• A 2kg mass is placed on a spring with spring constant k (k=5,000,000). The system
is placed on the surface of the moon. In this problem we want to determine how much the spring must be compressed in order for the mass to escape the gravitational potential of the moon.
• A) (5pts) Write the expression for the gravitational potential of the mass at the surface of the moon.
• B) (5pts) Determine the gravitational potential of the mass once it has escaped the moon’s pull.
kgMkmR moonmoon223 1035.7,1074.1
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Exam Prep Problem• A 2kg mass is placed on a spring with spring constant k (k=5,000,000). The system
is placed on the surface of the moon. In this problem we want to determine how much the spring must be compressed in order for the mass to escape the gravitational potential of the moon.
• C) (7pts) What must the velocity of the object be once it leaves the spring in order for the mass to escape the moon’s pull?
kgMkmR moonmoon223 1035.7,1074.1
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Exam Prep Problem• A 2kg mass is placed on a spring with spring constant k (k=5,000,000). The system
is placed on the surface of the moon. In this problem we want to determine how much the spring must be compressed in order for the mass to escape the gravitational potential of the moon.
• D) (8pts) How far must the spring be compressed in order for the mass to escape the moon’s pull?
kgMkmR moonmoon223 1035.7,1074.1
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Administrative Notes
• Exam II Monday 9:00-9:50am, OH 150.• HW Review Session Today 6:30 pm, OH218• Exam Prep Session FRIDAY, 5-8pm, OH218• Exam II covers Chapters 5-8
– 3 Problems– 1(6) Multiple Choice– 2 Problems– Get as many pts as possible as quickly as possible.– Exam will be harder than Exam I.
• Practice Exams posted• Exam solutions will be posted this morning.
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Outline
• Momentum and Force• Conservation of Momentum• Collisions• Impulse
• 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– Kepler’s 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
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Linear Momentum
• Linear momentum is defined as the product of an object’s mass and velocity.
• Units of momentum
• Velocity depends on reference frame, so does momentum.
vmp
vmp
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Linear Momentum
• A force is required to change the momentum of an object.
• Can calculate average Force, if you know t and change in momentum.
dt
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Example
• The speed of fastball is about 90 mph, and the speed of the ball (0.145kg) coming off of Ortiz’ bat for a home run is about 120mph. The ball is in contact with the bat for 1ms. What is the average Force exerted by Ortiz?
sm
sm
mph
mph
54110
4090
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Conservation of Momentum
• Momentum is important because, if no external Force acts on a system, it is a conserved quantity.
• For instance, for a two body problem, where we have a collision:
BBAAinitial vmvmP
''BBAAfinal vmvmP
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Conservation of Momentum for Two Objects
• Imagine we have two objects, A and B, which collide.• During the collision, A exerts a Force on B, changing the
momentum of B
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Is Momentum Always Conserved?
• Imagine a “system” of 2 objects. For instance, the baseball bat hitting the ball.
• Can we say that the momentum of the bat and ball are conserved from the time the ball is pitched to the time it lands in the stands?
• What about for the time of collision?
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Conservation of Momentum (many bodies)
• We considered 2 objects.• What about many objects?
• Two types of Forces can act on the system– Internal
– External
• So if all Forces are internal, then the total momentum of the system is conserved.
isystem pvmvmvmvmP
...44332211
.extsystem Fdt
Pd
iisystem Fdt
p
dt
Pd
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Law of Conservation of Momentum
• When the net external force on a system of objects is zero, the total momentum of the system remains constant.
• Or…• The total momentum of an isolated system of
objects remains constant• Where an isolated system refers to one on which
no external forces acts.
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Example
• A falling rock (10kg) is dropped from height of 5m.
• Is momentum conserved?• Consider rock alone
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Example
• Now consider Earth and Rock.
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Problem Solving w/ Momentum
• For a system where momentum is conserved, we first write the initial and then the final momentum of the system, in terms of all the objects in the system.
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Example
• A car (1000kg) going 10m/s rear ends your car (1000kg) when you are at a stop sign. Your bumpers lock and you travel forward together. Ignoring friction, and assuming your foot is off the brake, what speed do you go through the stop sign with?
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Example
• Suppose if instead of a car, it is a truck (6,000kg), going 10m/s that rear ends you. Ignoring friction, and assuming your foot is off the brake, what speed do you go through the stop sign with now?
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Example
Department of Physics and Applied Physics95.141, S2010, Lecture 15
Rocket Propulsion• Wall-e (50kg) moves by creating a makeshift rocket propulsion
system using a fire extinguisher (5kg).• Say Wall-E is moving away from EVE at a speed of 50m/s. He uses
the rocket to turn around and start moving towards EVE at 5m/s. If Wall-e uses up half of the total contents of the Fire Extinguisher (mass of contents=2.4kg), how fast must the CO2 come out of the nozzle?
Department of Physics and Applied Physics95.141, S2010, Lecture 15
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, S2010, Lecture 15
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, S2010, Lecture 15
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, S2010, Lecture 15
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, S2010, Lecture 15
What Did We Learn?
• Linear Momentum
• Conservation of Linear Momentum
• Collisions and Conservation of Momentum
• Impulse