Download Principle of Impulse and momentum

Principle of Work and Energy
T1 + SU1-2 = T2
Conservation of Energy
CHAPTER 15
Kinetics of a Particle: Impulse and Momentum
Objectives
1. To develop the principle of linear impulse and momentum
for a particle
2. To study the conservation of linear momentum for a particle
3. To analyze the mechanics of impact
v = ds/dt
a = dv/dt
dt = ds/v
dt = dv/a
ads = vdv
T1 + SU1-2 = T2
Principle of Work and Energy
ads = vdv
Principle of Linear Impulse and Momentum
a = dv/dt
Linear Impulse
Variable Force
Constant Force
+
=
Principle of Linear Impulse and Momentum
a particle
system of particles
ex1
100 kg stone is originally at rest on the smooth horizontal space.
If a towing force of 200 N, acting at an angle of 45o, is applied
to the stone for 10 s, determine the final velocity and the normal force
which the surface exerts on the stone during the time interval.
Principle of Impulse and momentum
+
Principle of Impulse and momentum
+
The 250 N crate is acted upon by a force having a variable magnitude
P = 100t, where t is in seconds. Determine the crate’s velocity 2 s after
P has been applied. The initial velocity is v1 = 1 m/s down the plane,
and mk = 0.3.
Principle of Linear Impulse and Momentum
a particle
system of particles
Conservation of Linear Momentum for a System of Particles
When the sum of the external impulses acting on a system of a particle
is zero,
Nonimpulsive force : - impulse that may be neglected
- considered equal to zero
Impulsive :
- forces that are very large and act for a very short
period of time
produce significant change in momentum
The force of the rackets on the ball is impulsive
The ball’s weight will have the negligible effect,  nonimpulsive
Ex1
Boxcar A : 15 Mg
Boxcar B : 12 Mg
If the car meets and couple together, determine
(a) the speed of both cars just after the coupling
(b) the average force between them if the coupling
takes place in 0.8 s
(a) the speed of both cars just after the coupling
Conservation of Linear Momentum
(b) the average force between them if the coupling takes place in 0.8 s
Principles of Impulse and Momentum
Ex 2
The 600 kg cannon shown fires a 4 kg projectile with a muzzle velocity
450 m/s relative to the ground. If firing takes place in 0.03 s, determine
(a) the recoil velocity of the cannon just after firing
(b) the average impulsive force acting on the projectile
The cannon support is fixed to the ground, and the horizontal recoil of
the cannon is absorbed by two springs.
Mc = 600 [kg]
Mp = 4
[kg]
(Vp )1 = 450 [m/s]
t = 0.03 [s]
Conservation of Linear Momentum
Priciples of Impulse and Momentum
Lab test 2
: 12/04/07 (Khamis)
Mid-Term 2 : 16/04/07 (Isnin)
Objectives
1. To develop the principle of linear impulse and momentum
for a particle
2. To study the conservation of linear momentum for a particle
3. To analyze the mechanics of impact
Impact
Impact occurs when two bodies collide with each other during a very
short period of time, causing relatively large (impulsive ) forces to be
exerted between the bodies.
Central Impact
Coefficient of Restitution e
e = 1 : Perfectly elastic impact
e = 0 : Plastic impact / inelastic impact
Ex
The bag A, having a mass of 6 kg, is released from rest at the position
q = 0o. After falling to q = 90o, it strikes an 18 kg box B. If the coefficient
of restitution between the bag and box is e = 0.5, determine
(i) the velocities of the bag and box just after impact
(ii) the loss of energy during collision
(i) the velocities of the bag and box
just after impact
Conservation of Energy
6 kg
Datum at q = 0o
6 kg
Conservation of Momentum
(i)
Coefficient of restitution
(ii)
Solving (i) and (ii),
(vA)2 = - 0.554 m/s
= 0.554 m/s 
(vB)2 = 1.66 m/s 
(ii) the loss of energy during collision
Loss of Energy
Oblique Impact
The particles move away with
velocities having unknown directions
and unknown magnitudes.
If v1 velocities are known;
(vA)2,
(vB)2
q2
f2
Ex
The smooth disks A and B, having a mass of 1 kg and 2 kg, respectively,
collide with the velocities shown in the figure. If e = 0.75, determine the x
and y components of the final velocity of each disk just after collision.
x components
y components
(i) for x components of the final velocity;
Conservation of “x” Momentum
(i)
Coefficient of Restitution (x)
Both disk are assumed to have components of velocity in the +x
direction after collision
(ii)
(i) for x components of the final velocity;
Solving (i) and (ii),
Ans.
Ans.
(ii) for y components of the final velocity;
Conservation of “y” Momentum
A man kicks the 200g ball such that it leaves the ground at an angle of 30o
With the horizontal and strikes the ground at the same elevation a distance
of 15m away. Determine the impulse of hiss foot F on the ball. Neglect the
Impulse caused by the ball’s weight while its being kicked.