department of physics and applied physics 95.141, s2010, lecture 15 physics i 95.141 lecture 15...

Department of Physics and Applied Physics95.141, S2010, Lecture 15

Physics I95.141

LECTURE 1510/27/10


Video Example


Video Example• How much Thermal Energy is generated in

reentry?• What is the average power generated in

reentry?

st

mA

v

kgM

mAltitude

v

f

sm

f

o

sm

o

300

620,7

134

4300

920,121

6.743,10

module

mR

G

kgM

kgNm

E

6Earth

11

24

1038.6

1067.6

1098.5

2

2


Energy Conservation

• Initial Mechanical Energy before re-entry:

• Mechanical Energy after re-entry:


Solve for Energies

• Change in Potential Energy

• Change in Kinetic Energy

• Change in Thermal Energy

• Power

r

mGMrU E)(


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


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?



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.


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


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


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

pdF


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


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


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


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?


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


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.


Example

• A falling rock (10kg) is dropped from height of 5m.

• Is momentum conserved?• Consider rock alone


Example

• Now consider Earth and Rock.


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.


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?


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?


Example


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?


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)


Collision and Impulse

• From Newton’s second law, we can write:

• This integral is known as the Impulse

dt

pdFnet


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


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


What Did We Learn?

• Linear Momentum

• Conservation of Linear Momentum

• Collisions and Conservation of Momentum

• Impulse

department of physics and applied physics 95.141, s2010, lecture 15 physics i 95.141 lecture 15...

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