Download Physics 106P: Lecture 1 Notes

Physics 101: Lecture 14
Impulse and Momentum
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Today’s lecture will cover Chapter 7.1 - 7.2
Physics 101: Lecture 14, Pg 1
Impulse and Momentum
Consider a ball hit by a baseball bat:
At t=t0: ball approaches bat with initial velocity v0
At t=tf: ball leaves the bat with final velocity vf
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During the time interval Dt=tf-t0 the ball is hit by the
bat, i.e. the bat exerts an average force Fave 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 2
Impulse and Momentum
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The effect on the motion of an object when a timevarying 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 = Fave Dt
SI unit: N s
To describe the response of an object to a given impulse we
need the concept of linear momentum:
p=mv
SI unit: kg m/s
Physics 101: Lecture 14, Pg 3
Impulse and Newton’s second law
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If there is a average net-force acting on an object during a
time interval Dt, the object experiences an acceleration, thus a
change in velocity, thus a change in momentum:
J = Fave,net Dt = m aav Dt = m (vf-v0)/Dt Dt =
= m vf – m v0 = pf – p0
In our example (neglect weight of ball):
the bat exerts force Fave on ball in time Dt
 impulse given to the ball => ball’s velocity changes
 ball’s momentum changes
From the change of velocity Fave,net can be determined.
Physics 101: Lecture 14, Pg 4
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
correct
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.
Physics 101: Lecture 14, Pg 5
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
correct
2. Downward
time
Physics 101: Lecture 14, Pg 6
Conservation of Linear Momentum
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Consider a system of colliding objects.
Two objects with masses m1 and m2 and initial velocities v01 and v02
collide:
If sum of average external forces acting on the balls is zero,
the total momentum of the system is conserved:
Fext,net Dt = Pf-P0 ; Pf=P0 if Fext,net =0 (isolated system)
Total momenta of the system: Pf=pf1+pf2 and P0=p01+p02
Physics 101: Lecture 14, Pg 7
Applying the Principle of Momentum
Conservation
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Decide which objects are included in the system.
Identify external and internal forces acting on the
system.
Verify that the system is isolated.
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 8
Impulse and Momentum Summary
Fave,netDt  J = pf – p0 = Dp
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For a single object….
Fave,net = 0  momentum conserved (Dp = 0)
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For collection of objects …
 Fave,ext = 0  total momentum conserved (DPtot = 0)
Physics 101: Lecture 14, Pg 9