Lecture 13: Momentum

Questions of Yesterday 1) A mass with speed v hits a horizontal spring and compresses it a distance d. If the the speed of the mass were doubled (2v) what would the compression distance be? a) 4d b) 2d c) d d) d/2 2) A mass on a spring is oscillating back and forth from x = -d to x = d? At what point in the oscillation is the speed of the mass the greatest? a) x = d b) x = -d c) x = 0 d) x = d and x = -d

Momentum Which ball do you want to have a game of toss with? Why? So, would you rather catch a speeding bullet? Why? MASS and VELOCITY affect force needed to stop a moving object in a given time interval

Momentum Linear Momentum (p) of a moving object is the product of its mass m and velocity v The more momentum an object has the more force you need to apply to stop it in a given time interval p = m*v UNITS kg*m/s p is a vector! Vector Equation! p x = m*v x p y = m*v y

Momentum & Newton’s 2nd Law Force is required to change an object’s momentum F net = ma The net force acting on an object is equal to the object’s change in momentum divided by the elapsed time of the force vv tt F net = m vv tt  mv) tt = = pp tt F net

Momentum & Newton’s 2nd Law Force is required to change an object’s momentum F net = ma vv tt F net = m vv tt  mv) tt = = pp tt F net MOMENTUM of an object is CONSERVED if F net = 0

Impulse IMPULSE (I) The change in an object’s momentum (  p) caused by a constant force (F) applied to the object over a given time interval (  t) I = F  t F  t =  p = mv f - mv i If F is only force acting on an object… Impulse = change in total momentum of the object I acts in same direction as F Units kg*m/s

Impulse & Varying Force  p = F  t F t

Impulse & Varying Force  p = F  t Impulse = Area under F vs t curve F t F t F av A = F av  t Impulse = Average Force * time interval  p = F av  t A =  p

Momentum & Impulse Concepts If a Mack truck and a Ford Escort have a head-on collision, which vehicle will experience… the greater force of impact? the greater impulse? the greater change in momentum? the greater acceleration?

Momentum & Impulse Concepts Would you rather get punched in the face with a bare fist or a boxing glove? In which case is the impulse delivered to your face greater? In which case is force on your face greater?

Momentum: Practice Problem A ball of mass 0.10 kg is dropped from rest from a height of 1.5 m. It rebounds from the floor to reach a height of 1.0 m. What impulse (magnitude and direction) was given to the ball by the floor? If the ball was in contact with the floor for 0.5 s, what was the force (magnitude and direction) exerted by the ball? What fraction of kinetic energy is lost in the collision?

Momentum: Practice Problem A 100-kg stuntman jumps from a balcony and falls 10.0 m before colliding with a pile of mattresses. If the mattresses are compressed 1.0 m before he is brought to rest… what is the average force exerted by the mattresses on the stuntman?

Momentum Conservation MOMENTUM of an object is CONSERVED if F net = 0 What happens in a collision? p i1 = m 1 v i1 p i2 = m 2 v i2

Momentum Conservation MOMENTUM of an object is CONSERVED if F net = 0 What happens in a collision? p i1 = m 1 v i1 p i2 = m 1 v i2 p f1 = ?p f2 = ? F 21  t =  p 1 = mv f1 - mv i1 F 12  t =  p 2 = mv f2 - mv i2 mv i1 + mv i2 = mv f1 + mv f2 3rd law: F 21 = -F 12

Momentum Conservation MOMENTUM of an object is CONSERVED if F net = 0 What happens in a collision? mv i1 + mv i2 = mv f1 + mv f2 If no net external force acts on a system of objects… The total momentum of the system remains constant in time p i = p f

Momentum: Practice Problem A rifle with a weight of 30 N fires a 10.0 g bullet with a speed of 300 m/s. -Find the recoil speed of the rifle -If a 700 N man holds the rifle firmly against his shoulder, find the recoil speed of the man and the rifle

Momentum: Practice Problem A 50-kg girl is standing on a 100-kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 2 m/s to the right relative to the plank. -What is her velocity relative to the surface of the ice? -What is the velocity of the plank relative to the surface of the ice?

Questions of the Day A 50-kg object is traveling with a speed of 100 m/s and a 100-kg object is traveling at a speed of 50 m/s. 1a) Which object has more momentum? 1b) Which object has more kinetic energy? a) 50-kg object b) 100-kg object c) they are equal 2) Would a head-on collision between two cars be more damaging to the occupants if the cars stuck together or if the cars rebounded upon impact? a) if the cars stuck together b) if the cars rebounded c) both collisions would be equally damaging d) it depends on the relative masses of the cars