Momentum, Impulse and Recoil

• A truck is rolling down a hill than a roller skater with the same speed; which has the greater momentum?

Momentum

Momentum

• Momentum is inertia in motion!

• Momentum = mass x velocity

• Momentum (p) = mv

• p= mass x speed (when direction is not important)

• A greater mass but the same speed will lead to a greater momentum

Decreasing Momentum

• Why does a car driven into a haystack at the same speed suffer less damage than one driven into a brick wall?

Impulse

• Impulse = F∆ t

• This is the force x time interval

• Impulse = change in momentum

• F ∆ t = ∆ (mv) [change in impulse = change in momentum

• If t increases and ∆ (mv) is constant then F decreases.

• This is the principle of an air bag in a car.

• Why does the boxer who moves back with a punch feel less pain than the boxer who moves into the punch?

Changes in Momentum

• The boxer increases the time taken for the impact and therefore reduces the force of the impact.

• Ft = change in momentum

• How does this runaway truck ramp use the laws of physics?

Bungee Jumping

• How does momentum and impulse relate to your changes of surviving a bungee jump?

• Ft = Impulse • Ft = ∆(mv)• The momentum, mv, is the amount gained

before the cord begins to stretch. Ft is the impulse the cord supplies to reduce the momentum to zero.

• Because the rubber cord stretches for a long time, a large time interval t ensures that a small average force F acts on the jumper.

• The cord typically stretches to about twice the original length during the fall.

Starter Questions

• How is the recoil of a rifle or cannon related to momentum conservation?

• A man is stranded in the middle of an ice rink that is perfectly frictionless. How can he get to the edge?

Conservation of Momentum• When the cannon is fired the

force on the cannonball inside the cannon barrel is equal and opposite to the force causing the cannon to recoil.

• Before the firing of the system is at rest and the momentum is zero.

• After the firing the net momentum, or total momentum, is still zero. Net momentum is neither gained nor lost.

Law of Conservation of Momentum

• In the absence of an external force, the momentum of a system remains unchanged.

• If a system undergoes changes wherein all the forces are internal, e.g. in atomic nuclei undergoing radioactive decay, cars colliding, or stars exploding, the net momentum remains constant.

• A bullet of mass 50g is fired from a gun of mass 2.0kg at a speed of 450 m/s. Calculate the speed of the recoil of the gun.

“In any interaction between two (or more objects) the total momentum of the objects remains constant”

Pi = PF

Recoil

Recoil of Gun

• Total momentum before and after is zero (as there is no velocity to start with).

• Momentum of bullet = Momentum of gun

Recoil Question

• A bullet of mass 0.01kg moves horizontally with a speed of 400m/s and embeds itself in a block of mass 0.39kg that is initially at rest on a frictionless table. Find the final velocity of the bullet and the block.

• Runaway truck ramp: http://www.northlight-images.co.uk/content_images/photography_tour/mon_5.jpg

• Truck: http://geoimages.berkeley.edu/geoimages/BainCalif/CAL400/runaway.jpg

• Roller Skater: http://www.mchenrycountyblog.com/uploaded_images/Roller-skates-715946.jpg

• Haystack: http://floridalawfirm.com/haystack.gif

• Brick wall: http://www.dailyhaha.com/_pics/car_crash_brick_wall.jpg

• Boxer avoids punch: http://cache.daylife.com/imageserve/01iL0EYd2c7Hd/610x.jpg

• Boxer lands punch: http://www.chinadaily.com.cn/sports/images/attachement/jpg/site1/20071205/001aa018ff9c08c0a6df0c.jpg

• Bungee Jumpers: http://uk.geocities.com/osfuk/osf/bungee.html

• Cannon firing: http://www.ottoleffler.com/psd/portfolio/Canon/ist2_2437935_fire_away.jpg

• Gun Recoil Pic: http://farm1.static.flickr.com/67/157553435_39e61a5113.jpg?v=0