phys16 – lecture 21

PHYS16 – Lecture 21

Ch. 9 Momentum and Collisions

• Linear Momentum– Related to Newton’s second law– Rocket Propulsion

• Momentum Conservation• Collisions– Elastic vs. Inelastic– 1D and 2D

• Impulse

Ch. 9 Momentum & Collisions

Momentum pre-question

• Consider two carts on a frictionless air track with masses m and 2m. If you push the lower mass cart for 3 s and then the other cart for the same length of time and with the same force, which cart undergoes the larger change in momentum?A) Cart with mass mB) Cart with mass 2mC) Change in momentum is the same for bothD) There is not enough information

Solve Problems with Collisions

• Read problem carefully!• Draw a picture.• Write down given quantities and what you want

to solve for.• Find the correct equation (conservation of

momentum and possibly conservation of energy).

• Do the math and solve!

Perfectly Elastic Collision

• A 1.00-kg ball traveling at 3.00 m/s collides with a 3.00-kg ball traveling at 0.500 m/s. If after a perfectly elastic collision the 1.00-kg ball is traveling at -0.750 m/s, how fast is the second ball going? How do we check to see if it is perfectly elastic?

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Perfectly Inelastic Collision

• How fast would a 5-g fly have to be traveling to slow a 1900-kg car traveling at 55 mph to 50 mph if the fly just splatted across the windshield?

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Superball vs. Basketball

• Drop a superball and basketball together. How high does the superball bounce?

• Homework problem…

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For Problems with multiple parts…

• Follow the steps for solving problems as before

• When you get to what equation to use break the problem into parts – usually chronologically – and solve each part

• Then do the math as before…

Click-Clack

• In a click-clack if all balls have equal mass and I take one ball out and put it at height 4 m, how high should the ball on the other side go?A) 4 mB) 2 mC) 1 mD) 0 mE) Not enough information

http://www.brucegray.com/images/clickclack.jpg

Click-Clack

http://www.brucegray.com/images/clickclack.jpg

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Click-Clack

• In a click-clack if all balls have equal mass and I take one ball out and put it at height 4 m, how high should the ball on the other side go?A) 4 mB) 2 mC) 1 mD) 0 mE) Not enough information

http://www.brucegray.com/images/clickclack.jpg

Smith & Wesson

• On homework there is a problem about how far a chair slides when a bullet gets shot into it. What demo does this remind you of?

• What are the parts you will need to know?

2D collisions – How to solve problems

• Separate vectors into x and y components• Solve two equations– Conservation of momentum in x and– Conservation of momentum in y

• If perfectly elastic get a third equation– Conservation of energy

2D Collisions• Need to add 2D vectors• Assume masses of two objects equal– Before

– AfterA

B

C

2D Collisions – Predict vectors, assume masses are equal

A

B

2D Collision problem• A 0.25 kg hockey puck traveling at 1.5 m/s strikes a stationary

puck with the same mass. If the first puck exits at 30 degrees and 0.75 m/s, what is the direction of the second puck?

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tan

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)cos()cos(

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3. Impulse

• Impulse describes the change in momentum– Good for describing what happens during a collision

• Example: – What is momentum of 0.5 kg ball dropped from 5 m just

before it hits the floor?– If the velocity after it hits the floor is +8 m/s upward, what

is the impulse?– If the interaction lasts 0.01 s, what was the average Force?

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During Collisions…

• Baseball• Soccer ball• Water balloon?

http://www.youtube.com/watch?v=pQ9NiazPYI8http://www.youtube.com/watch?v=90VyvOhPmA0&NR=1&feature=fvwphttp://www.youtube.com/watch?v=jjE8SQG8AwI&feature=related

Discussion

• Why does an airbag reduce injury?• What is better in bungee jumping- a stiff cable

that won’t break at high forces or a stretchy cable?

• Why should a boxer “ride the punch” and not stiffen her neck muscles?

Momentum pre-question

• A 0.50 kg ball accelerates from rest at 10.0 m/s2 for 2.0 s. It then collides with and sticks to a 1.0 kg ball that is initially at rest. After the collision, how fast are the balls going?A) 3.3 m/sB) 6.7 m/sC) 10 m/sD) 15 m/sE) None of the above.

Momentum pre-question

• Consider two carts on a frictionless air track with masses m and 2m. If you push the lower mass cart for 3 s and then the other cart for the same length of time and with the same force, which cart undergoes the larger change in momentum?A) Cart with mass mB) Cart with mass 2mC) Change in momentum is the same for bothD) There is not enough information

Conclusions

• Momentum

• Momentum Conservation

• Elastic vs. Inelastic Collisions• Impulse

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