Physics 101: Lecture 14, Pg 1 Physics 101: Lecture 14 Impulse and Momentum l Today’s lecture will cover Chapter

Physics 101: Lecture 14, Pg 2 Impulse and Momentum l Consider a ball hit by a baseball bat: At t=t 0 : ball approaches bat with initial velocity v 0 At t=t f : ball leaves the bat with final velocity v f During the time interval  t=t f -t 0 the ball is hit by the bat, i.e. the bat exerts an average force F ave on the ball. To describe the effect of such a time-varying force on the motion of an object we introduce two new concepts: Impulse and Momentum

Physics 101: Lecture 14, Pg 3 Impulse and Momentum l The effect on the motion of an object when a time- varying force is applied will be the larger the longer the force is acting on the object and the larger the larger the force. This observation is described by the concept of impulse: J = F ave  t SI unit: N s To describe the response of an object to a given impulse we need the concept of linear momentum: p = m v SI unit: kg m/s

Physics 101: Lecture 14, Pg 4 Impulse and Newton’s second law If there is a average net-force acting on an object during a time interval  t, the object experiences an acceleration, thus a change in velocity, thus a change in momentum: J = F ave,net  t = m a av  t = m (v f -v 0 )/  t  t = = m v f – m v 0 = p f – p 0 In our example (neglect weight of ball): the bat exerts force F ave on ball in time  t  impulse given to the ball => ball’s velocity changes  ball’s momentum changes From the change of velocity F ave,net can be determined.

Physics 101: Lecture 14, Pg 5 Conceptual Question Two identical balls are dropped from the same height onto the floor. In case 1 the ball bounces back up, and in case 2 the ball sticks to the floor without bouncing. In which case is the impulse given to the ball by the floor the biggest? 1. Case 1 2. Case 2 3. The same The impulse-momentum theory says that the impulse that acts on an object is given by the change in the momentum of the object, and this change is proportional to the change in velocity. The ball that sticks has a velocity of downward to zero, but the velocity of the ball that bounces goes downward then upward. This change in momentum is greater and therefore has a greater impulse on it. correct

Physics 101: Lecture 14, Pg 6 Conceptual Question In both cases of the above question, the direction of the impulse given to the ball by the floor is the same. What is this direction? 1. Upward 2. Downward time correct

Physics 101: Lecture 14, Pg 7 Conservation of Linear Momentum l Consider a system of colliding objects. Two objects with masses m 1 and m 2 and initial velocities v 01 and v 02 collide: If sum of average external forces acting on the balls is zero, the total momentum of the system is conserved: F ext,net  t = P f -P 0 ; P f =P 0 if F ext,net =0 (isolated system) Total momenta of the system: P f =p f1 +p f2 and P 0 =p 01 +p 02

Physics 101: Lecture 14, Pg 8 Applying the Principle of Momentum Conservation l Decide which objects are included in the system. l Identify external and internal forces acting on the system. l Verify that the system is isolated. l Initial and final momenta of the isolated system can be considered to be equal. Application: velocities of colliding objects after collision

Physics 101: Lecture 14, Pg 9 Impulse and Momentum Summary F ave,net  t  J = p f – p 0 =  p l For a single object…. è F ave,net = 0  momentum conserved (  p = 0) l For collection of objects … è  F ave, ext = 0  total momentum conserved (  P tot = 0)