Transcript L16

Impulse and Momentium
 Principle of Impulse and
Momentum
 Central Impact
Union College
Mechanical Engineering
MER045: Dynamics of Mechanisms
1
Energy and Momentum Methods
F=ma
+
Principles of Kinematics
Impulse and
Momentum Methods
Work and
Energy Methods
Integration of Force
with respect to Displacements
Integration of Force with
Respect to Time
Force, Mass, Velocity
Displacement
Force, Mass, Velocity,
Time
Union College
Mechanical Engineering
MER045: Dynamics of Mechanisms
2
Principle
 Impulse and Momentum are used to
solve problems involving




force
mass
velocity
time
 Consider a particle acted on by a force
 d

F  m  v 
dt
 Where mv is the LINEAR MOMENTUM
Union College
Mechanical Engineering
MER045: Dynamics of Mechanisms
3
Impulse and Momentum
Equation
 Integrating Newton’s Law with respect
t2 


to time
m  v1   F  dt  m  v 2
t1
Lin e arIm pu lse
 Linear impulse is a vector quantity
 The Final Momentum mv2 of a particle
may be obtained by adding vectorally its
initial momentum mv1 and the impulse
of the force during the time interval
considered
Union College
Mechanical Engineering
MER045: Dynamics of Mechanisms
4
Example 1
An automobile weighing 4000lb is driven down a 5° incline at a
speed of 60 mi/hr when the brakes are applied, causing a
constant total braking force (applied by the road on the tires)
of 1500lb.
Determine the time required for the automobile to come to a
stop.
Union College
Mechanical Engineering
MER045: Dynamics of Mechanisms
5
Example 1 - Diagram
Union College
Mechanical Engineering
MER045: Dynamics of Mechanisms
6
Example 2
An airline employee tosses a 30lb suitcase with a horizontal
velocity of 10 ft/s onto a baggage carrier. The carrier can roll
freely and is initially at rest.
Determine the velocity of the carrier after the suitcase has
slid to a relative stop on the carrier.
Union College
Mechanical Engineering
MER045: Dynamics of Mechanisms
7
Example 2 - Diagram
Union College
Mechanical Engineering
MER045: Dynamics of Mechanisms
8