Transition From Forces to Conservation Laws - Lecture Slides | PHYSICS 207, Assignments of Physics

Download Transition From Forces to Conservation Laws - Lecture Slides | PHYSICS 207 and more Assignments Physics in PDF only on Docsity! Page 1 Physics 207 – Lecture 11 Physics 207: Lecture 11, Pg 1 "Professor Goddard does not know the relation between action and reaction and the need to have something better than a vacuum against which to react. He seems to lack the basic knowledge ladled out daily in high schools." New York Times editorial, 1921, about Robert Goddard's revolutionary rocket work. "Correction: It is now definitely established that a rocket can function in a vacuum. The 'Times' regrets the error." New York Times editorial, July 1969. Physics 207: Lecture 11, Pg 2 Partial Survey Summary Lecture
Too many slides that come too quickly
More problem solving on white board
Too much time spent on “interactive problems but, when used, not enough time spent on explanation
More demos Physics 207: Lecture 11, Pg 3 Another example with friction and pulley
Three 1 kg masses are connected by two strings as shown below. There is friction between the stacked masses but the table top is frictionless.
Assume the pulleys are massless and frictionless.
What is T1 ? M M M T1 friction coefficients µs=0.4 and µk=0.2 Physics 207: Lecture 11, Pg 4 Physics 207, Lecture 11, Oct. 10 Agenda: Assignment:
Read through Chapter 10
MP HW5 available now, due Wednesday 10/17, 11:59 PM • Chapter 9: Momentum & Impulse  Momentum conservation  Collisions  Impulse Physics 207: Lecture 11, Pg 5 Impulse & Linear Momentum
Transition from forces to conservation laws Newton’s Laws  Conservation Laws Conservation Laws  Newton’s Laws They are different faces of the same physics phenomenon. NOTE: We already have studied “impulse” and “momentum” but we have not explicitly named them as such Physics 207: Lecture 11, Pg 6 Lecture 11, Example 1 A 2 kg cart initially at rest on frictionless horizontal surface is acted on by a 10 N horizontal force along the positive x-axis for 2 seconds what is the final velocity?
F is in the x-direction F = ma so a = F/m = 5 m/s2
v = v0 + a t = 0 m/s + 2 x 5 m/s = 10 m/s (+x-direction) What if the mass had been 4 kg? What is the new final velocity? Page 2 Physics 207 – Lecture 11 Physics 207: Lecture 11, Pg 7 Twice the mass
Same force
Same time
Half the acceleration
Half the velocity ! ( 5 m/s ) Physics 207: Lecture 11, Pg 8 Example 1
Notice that the final velocity in this case is inversely proportional to the mass (i.e., if thrice the mass….one-third the velocity).
It would seems that mass times the velocity always gives the same value. (Here is it always 20 kg m/s.) Physics 207: Lecture 11, Pg 9 Example 1
There many situations in which the product of “mass times velocity” is a constant and so we give a special name, “momentum” and associate it with a conservation law. (Units: kg m/s or N s)
A force applied for a certain period of time can be plotted and the area under this curve is called “impulse” Physics 207: Lecture 11, Pg 10 Example 1 with Action-Reaction
Now the 10 N force from before is applied by person (me) and I happen to be standing on a frictionless surface as well and I am also initially at rest.
What is the force on me and for how long ? Physics 207: Lecture 11, Pg 11 Example 1 with Action-Reaction
The 10 N force from before is applied by person (me) and I happen to be standing on a frictionless surface as well and I am also initially at rest.
What is the force on me and for how long ?
10 N but in the –x direction
2 seconds Physics 207: Lecture 11, Pg 12 Example 1 with Action-Reaction
The 10 N force from before is applied by person (me) and I happen to be standing on a frictionless surface as well and I am also initially at rest.
What is the force on me and for how long ?
10 N but in the –x direction
2 seconds
And what is my final velocity (V) if I’m mass “M” ?
V = a’ t = F/M t in the –x direction Page 5 Physics 207 – Lecture 11 Physics 207: Lecture 11, Pg 25 Lecture 11, Exercise 2 Momentum Conservation A. Box 1 B. Box 2 C. same
Two balls of equal mass are thrown horizontally with the same initial velocity. They hit identical stationary boxes resting on a frictionless horizontal surface.
The ball hitting box 1 bounces elastically back, while the ball hitting box 2 sticks.  Which box ends up moving fastest ? 1 2 Physics 207: Lecture 11, Pg 26 A perfectly inelastic collision in 2-D
Consider a collision in 2-D (cars crashing at a slippery intersection...no friction). v1 v2 V before after m1 m2 m1 + m2
If no external force momentum is conserved.
Momentum is a vector so px, py and pz Physics 207: Lecture 11, Pg 27 Elastic Collisions
Elastic means that the objects do not stick.
There are many more possible outcomes but, if no external force, then momentum will always be conserved
Start with a 1-D problem. Before After Physics 207: Lecture 11, Pg 28 Elastic Collision in 1-D v1b v2b before x m1 m2 v1a v2a after m1 m2 Physics 207: Lecture 11, Pg 29 Force and Impulse (A variable force applied for a given time)
Gravity: usually a constant force to an object
Springs often provides a linear force (-k x) towards its equilibrium position
Collisions often involve a varying force F(t): 0  maximum  0
We can plot force vs time for a typical collision. The impulse, J, of the force is a vector defined as the integral of the force during the time of the collision. Physics 207: Lecture 11, Pg 30 Force and Impulse (A variable force applied for a given time) F ∫∫∫ === ptt pddtdtpddtFJ rr rr )/(
J reflects momentum transfer t ti tf ∆t Impulse J = area under this curve ! (Transfer of momentum !) Impulse has units of Newton-seconds Page 6 Physics 207 – Lecture 11 Physics 207: Lecture 11, Pg 31 Force and Impulse
Two different collisions can have the same impulse since J depends only on the momentum transfer, NOT the nature of the collision. ∆t F t F t ∆t same area ∆t big, F small ∆t small, F big Physics 207: Lecture 11, Pg 32 Average Force and Impulse ∆t F t F t ∆t ∆t big, Fav small ∆t small, Fav big Fav Fav Physics 207: Lecture 11, Pg 33 Lecture 11, Exercise 3 Force & Impulse A. heavier B. lighter C. same D. can’t tell
Two boxes, one heavier than the other, are initially at rest on a horizontal frictionless surface. The same constant force F acts on each one for exactly 1 second. Which box has the most momentum after the force acts ? F F light heavy Physics 207: Lecture 11, Pg 34 Boxers: Physics 207: Lecture 11, Pg 35 Back of the envelope calculation (1) marm~ 7 kg (2) varm~7 m/s (3) Impact time ∆t ~ 0.01 s  Impulse J = ∆p ~ marm varm ~ 49 kg m/s  F ~ J/∆t ~ 4900 N (1) mhead ~ 6 kg  ahead = F / mhead ~ 800 m/s 2 ~ 80 g !
Enough to cause unconsciousness ~ 40% of fatal blow tFdtFJ t ∆== ∫ avg rrr Physics 207: Lecture 11, Pg 36 Woodpeckers: Page 7 Physics 207 – Lecture 11 Physics 207: Lecture 11, Pg 37 During "collision" with a tree, nominally ahead ~ 600 - 1500 g!! How do they survive? • Jaw muscles act as shock absorbers • Straight head trajectory reduces damaging rotations (rotational motion is very problematic) Physics 207: Lecture 11, Pg 38 Physics 207, Lecture 11, Oct. 10 Assignment:
Read through Chapter 10
MP HW5 available now, due Wednesday 10/17, 11:59 PM