Physics 1A. Lecture 8B

Transcription

1 Physics 1A Lecture 8B

2 Review of Last Lecture Momentum is defined as: It is a vector quantity Newton s original 2 nd law stated: Change in momentum with time is equal to applied force Impulse is change in momentum caused by force acting over time: Impulse is a vector quantity with dimensions: M L T 1 For any system, internal forces do not change the system s total momentum

3 Newton s 1 st Law: In the absence of a net external force, there is no change in the total momentum of a system This is the Law of Conservation of Momentum

4 Examples of Systems block on an inclined plane 2 out of 3 dentists A DNA Molecule A Galaxy

5 Examples of Systems block on an inclined plane 2 out of 3 dentists A DNA Molecule A Galaxy

6 Newton s 1 st Law: In the absence of a net external force, there is no change in the total momentum of a system This is the Law of Conservation of Momentum

7 Newton s 1 st Law: In the absence of a net external force, there is no change in the total momentum of a system This is the Law of Conservation of Momentum

8 Collisions What happens when two objects collide?

9 Collisions magic happens

10 Collisions?

11 CERN: Large Hadron Collider instrument that discovered the Higgs boson

12 Initial magic Final Impulse on ball 1: Newton s 3 rd Law Impulse on ball 2:

13 Initial magic Final

14 Momentum Conservation For a given system (any collection of objects), the change in the total momentum is equal to the externally applied force (internal forces don t matter) If there is no net external force, total momentum is conserved (constant)

15 Notes on Momentum Conservation Conservation of momentum comes from Newton s 3 rd law of motion applies to all interactions The nature of the interaction force doesn t matter Momentum gained by some parts of system is equal to momentum lost by other parts Conservation of momentum is a vector law direction and magnitude must be considered

16 Applying Momentum Conservation to Physics Problems 1. Set up the problem draw a figure, predict the outcome, write down the quantities you are provided and the quantity(ies) to determine; choose a coordinate system 2. Identify the relevant system (e.g., all interacting objects) 3. Calculate initial and final momenta (p i and p f ) for each coordinate axis 4. Determine if there are any external forces acting (e.g., gravity); if so, calculate F ext Δt (impulse) acting on system for each coordinate axis 5. Using Σp f Σp i = F ext Δt for each coordinate axis, solve for unknowns 6. Check your answer (dimensions and expectations)

17 Example S vs. P Student Professor

18 Example sticky collision 3 kg adhesive 5 kg 3 kg 5 kg Before After A block of mass 3 kg with speed v 1 = 4 m/s comes into contact with another block. Adhesion between the two blocks causes them to stick together, so that the pair move together with speed v 12. There are no other forces acting. What is this final speed?

19 Example sticky collision 3 kg adhesive 5 kg 3 kg 5 kg What is the system? Both blocks What are your expectations for the motion? Before After

20 Example sticky collision 3 kg adhesive 5 kg 3 kg 5 kg Initial and final momenta: Σp i = m 1 v 1 +m 2 v 2 = (3 kg)(4 m/s) = 12 kg m/s Σp f = m 1 v 1 + m 2 v 2 = (m 1 + m 2 )v 12 = (3 kg + 5 kg)v 12 = 8 v 12 v 12 = 1.5 m/s Before After Note: adhesive force didn t matter!

21 Example sticky collision 3 kg adhesive 5 kg 3 kg 5 kg What about kinetic energy? K i = (m 1 v 1 2 +m 2 v 22 )/2 = (3 kg)(4 m/s) 2 /2 = 24 J K f = (m 1 + m 2 )v 122 /2 = (3 kg + 5 kg)v 122 /2 = (8 kg)(1.5 m/s) 2 /2 = 9 J Before After Note: That s where adhesive force matters!

22 Example sticky collision 3 kg adhesive 5 kg 3 kg 5 kg Same setup, but now add gravity, assume sticking takes 0.5 seconds. What is velocity just after objects start moving? What are your expectations? Before After

23 Example sticky collision 3 kg adhesive Initial and final momenta: Σp i = m 1 v 1 +m 2 v 2 = 12 kg m/s Before 5 kg 3 kg 5 kg After Σp f = m 1 v 1 + m 2 v 2 = 8 v 12 ΣF ext Δt = m 1 gδt + m 2 gδt = (3kg+5kg)(9.8m/s 2 )(0.5s) = 39 kg m/s p f - p i = F ext Δt => v 12 = 6.4 m/s

24 Energy and momentum conservation In the case of a closed system with no transfer of energy to the environment and no external forces, both momentum and energy are conserved (Remember: E = kinetic energy + potential energy)

25 Example S vs. P Student Professor Are you sure there is no potential energy here? What happened???

26 Muscular Potential Energy Our muscle cells can covert chemical energy (sugars) into mechanical work we are constantly carrying potential energy around with us!

27 Example S vs. P Student Professor How much muscular work was done? 18 J

28 Types of Collisions Elastic: Momentum and Kinetic Energy are both conserved Inelastic: Momentum conserved, Kinetic Energy is lost Perfectly Inelastic: Objects stick, Momentum conserved, Kinetic Energy is maximally lost Superelastic: Momentum conserved, Kinetic Energy is gained

29 Types of Collisions K(initial) + Q = K(final) Inelastic collisions: Q < 0 Elastic collisions: Q = 0 Super-elastic collisions: Q > 0

30 For Next Time (FNT) Continue working on reading and homework for Chapter 8