Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Physics I 95.141 LECTURE 12...

Department of Physics and Applied Physics95.141, F2010, Lecture 12

Physics I95.141

LECTURE 1210/18/10


Work Done by a Spring

• The force exerted by a spring is given by:

kxFspring

Hooke’s Law


Example Problem

• How much work must I do to compress a spring with k=20N/m 20cm?


Exam Prep Problem

• A 5,000 kg rocket is launched from the Earth’s surface at a constant velocity (v=50m/s). Assume there is a velocity dependent drag force (FD=-10v2).

– A) (5pts) What is the Force required to move the rocket at

the surface of the Earth? 1,000 km above the Earth’s surface?

– B) (5pts) What is the Work done by air resistance over the 1,000km?

– (C) (10pts) What is the Work done by Force responsible for moving the rocket over those 1,000km?

kgMmR EARTHEARTH246 1098.5,104.6


Exam Prep Problem

• A 5,000 kg rocket is launched from the Earth’s surface at a constant velocity (v=50m/s).

– A) (5pts) What is the Force required to move the rocket at the surface of the Earth? 1,000 km above the Earth’s surface? Ignore air resistance.



Exam Prep Problem


– B) (5pts) What is the Work done by air resistance over the

1,000km?



Exam Prep Problem


– C) (10pts) What is the Work done by Force responsible for

moving the rocket over those 1,000km?



Review of Dot Products• Say we have two vectors

• What is angle between them?

kjiB

kjiA

ˆ4ˆ7ˆ4

,ˆ3ˆ2ˆ6


Outline

• Work-Energy Theorem• Conservative, non-conservative Forces

• 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


Energy

• One of the most powerful concepts in science, used to solve complicated problems in basically all fields of Engineering, Chemistry, Materials Science, Physics…

• For the purpose of this chapter, we will define Energy as: The ability to do work.– This means something has energy if it can exert a

force over a distance

• We will begin by looking at translational kinetic energy


Translational Kinetic Energy

• Kinetic: associated with motion• Translational: motion in a line or trajectory (as

opposed to circular/rotational motion)


Moving Car

• Say a car starts at some velocity v1, and, with a constant net Force Fnet applied to it, accelerates to a velocity v2 over a distance d.


Kinetic Energy

• The net work done on the car results in a change of the car’s kinetic energy (K). The car’s energy (also in Joules), changes by an amount equal to the net work done on the car.


Work Energy Principle

• The net work done on an object is equal to the change in the object’s kinetic energy.


Example

• What is the net Work required to accelerate a 1000kg car from rest to 20 m/s?

• What about from 20 m/s to 40 m/s?


Example

• What about the net Work required to stop this car when it is going 40 m/s?


Energy of a Spring• A spring (k=400N/m) is compressed 10cm, and a mass (m=2kg) is

place in front of the spring. How much work does the spring do on the mass after the spring is released?

x=-10cm


Compressed Spring

• What is the kinetic energy (and velocity) acquired by the mass when it separates from the released spring at x=0?


What about Friction?

• Say we assume a constant frictional force (5N) on the mass as it is pushed by the spring. Does work-energy theorem still hold?


Spring problem

• Find spidey-k


Work Done to Extend Spidey-web• d≈500m

• vo=25m/s

• Mtrain=181,000


Kinetic Energy of Train


Work-Energy Principle

• Energy is the ability to do work– Train’s kinetic energy does work on Spiderman’s springs

• Work and Energy have the same units• Kinetic Energy proportional to mass and the square

of velocity• Both Work and Energy are scalar quantities.• Can be applied to a particle, or a mass that can be

approximated by a particle…where internal motion is insignificant.

• Why do we use Work/Energy here and not Kinematic equations?


Conservative and Non-Conservative Forces

• A Conservative Force:– The work done by the force on an object moving from

one point to another depends only on the initial and final positions of the object, and is independent of the particular path taken.

• A conservative force is only a function of position


Is Gravity a Conservative Force?• Imagine two scenarios:

h

ddh


Alternative Definition

• A force is conservative if the net work done by the force on an object moving around a closed path is zero.


Conservative Forces

• The work done by a conservative force is recoverable– The work done by the object (on something else) on a

given path is equivalent to the work done by the something else on the object on its return trip.

– This means that the net work done on the object over the closed loop is zero, which means, from the work-energy theorem, that the change in energy of the object is zero.

– Energy is conserved!


Springs

• Is the Force exerted by a spring a conservative force?


What about Friction?

• Is friction a conservative Force?

d

d


Non-Conservative Forces

• For friction, the work done by friction on an object moving around a closed loop will never be zero.

• This work is not recoverable

• Work done by friction (or any nonconservative Force) depends on path between two points


Non-Conservative Forces

• Work done by non-conservative force depends on path


What about air resistance?

• Move from point A to point B, either by path 1 or path 2, at constant velocity (FD=-bv).

A BPath 1

Path 2

R


What about air resistance?

• Move from point A to point B, same path, but different speeds, (FD=-bv).

A BPath 1

2R


What did we learn today?

• How we can use Energy/Work to understand physical systems

• Power of Work/Energy is that we don’t have to know anything about acceleration, or even the complicated kinematic equations that would go with spring/mass systems or air resistance, etc…

• All we need is energy!

Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Physics I 95.141 LECTURE 12...

Documents

Transcript of Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Physics I 95.141 LECTURE 12...