Conservation of Momentum PDF

Preview

Summary

Dr. Thomas...

Description

Conservation of Momentum Momentum  Quantity of motion that an object possesses  Linear momentum: product of object’s mass and its velocity  M = mv (units: kg*m/s)  Angular momentum: product of object’s moment of inertia and its angular velocity  H = Iw (kg*m/s2) Linear Momentum  How do we change momentum linearly?  Change mass (usually not affected) (but with garbage truck, can change if it is empty or full)  Change velocity (happens during collisions)

M1=M2 m1v1 =

Conservation of Momentum  Related to Newton’s Law I  Recall: if no external forces act on a body then the velocity of the body remains constant  i.e.: in the absence of external forces, the total momentum of the system remains constant (m1=m2) Impulse  External forces acting on an object to change momentum KNOW FOR MIDTERM  Dependent on:  Magnitude of force  Time it acts (how long the force is applied)  J = Ft (J is impulse) (units: Ns)  Relation b/w impulse and momentum related to Newton’s Law II  Impulse is what allows momentum to change from initial state to final state  Changes in momentum may result from  Small F acting for a long time  Large F acting quickly  Ex: hitting a baseball- large force from bat acting very quickly on the ball  Can we manipulate impulse? Yes- manipulating force, time of collision  Larger impulse = greater change in momentum = greater jump height  Vertical jump: countermovement (bending knees- storing energy- stretch/shortening cycle)  Increase t  not practical b/c force actually decreases as time increases (you are spending more energy to maintain the countermovement than you would get in return)  Must find tradeoff b/w F and t  Landing: landing stiff legged dec. time. Flexing inc. time over which force is applied  Landing is from touch-down to when you stop decelerating (transition from knees bent to standing)  Stiff-legged has larger implications for injury- want muscles to absorb impact (not bones and ligs) Angular Momentum  How do we manipulate angular momentum?  Change I or omega  To conserve (H stays constant)  inc I = dec w; dec I = inc w  Rotating bodies  Three axes passing through COM  Transverse: L to R and || (parallel) to floor (somersault)  Frontal: front to back and || to floor (tilt)  Longitudinal: head through feet (twist)  How do gymnasts initiate somersaults in the air? How do they stop their rotations?  Exploit conservation of angular momentum  Start: (position: tall, upright) (mechanics: large I, low w) (impression: traveling up not rotating)  Middle: (position: tucked or pike) (mechanics: dec I, inc w) (impression: started somersault in air)  End: (position: straightening) (mechanics: inc I, dec w) (impression: stopping rotation to land)  How do gymnasts generate twists for aerial skills?

 Contact  Tilt Contact Twist  While in contact w/ ground  Generate moment about longitudinal axis  Ex: turn shoulder during take-off (Newton’s Law II)  Causes GRF vector to pass through where you are turning toward, not COM (causes you to start turning when you leave ground)  Can manipulate rate of twist by applying conservation of angular momentum  Pulls arms in to dec. I  results in increased w Tilt Twist  When somersaulting if body is tilted away from vertical it will twist  Required to keep angular momentum constant about all axes  How can body be tilted?  Raising or lowering one arm  Turning shoulders when body is piked  Extending from pike asymmetrically (asymmetry is KEY)  Important  ONLY works when somersaulting  More tilt = faster twist  Twist normally can be stopped by reverse process  Movements to produce twist are often subtle  Can be combined with another method of twist generation (contact twist) to enhance twist Long Jump  Jumpers can have 15kgm2/s of angular momentum about transverse axis  Goal: land with feet forward not rotated back  Have to rotate arms and legs to generate angular momentum...