12202.
Determine the time needed for the load at B to attain a
speed of 8 m> s, starting from rest, if the cable is drawn into
the motor with an acceleration of 0.2 m> s2.
A
vA
SOLUTION
4 sB + sA = l
B
4 nB = - vA
4 aB = - aA
4 aB = - 0.2
aB = - 0.05 m> s
*1540.
The 200-g projectile is fired with a velocity of 900 m>s
towards the center of the 15-kg wooden block, which rests
on a rough surface. If the projectile penetrates and
emerges from the block with a velocity of 300 m>s, determine the velocity of the
1666.
Determine the angular velocity of the gear and the velocity
of its center O at the instant shown.
A
45
4 ft/s
SOLUTION
General Plane Motion: Applying the relative velocity equation to points B and C
and referring to the kinematic diagram of the gear
1687.
If crank AB is rotating with an angular velocity of
vAB = 6 rad> s, determine the velocity of the center O of
the gear at the instant shown.
0.6 m
B
C
O
0.4 m
vAB
A
SOLUTION
Rotation About a Fixed Axis: Referring to Fig. a,
vB = vAB rB = 6(0.4) = 2.
Chapter 15 Kinetics of a Particle: Impulse and Momentum
r
r
Liner momentum of a particle: L = mv . It is a vector.
t2 r
r
r
Principle of Linear Impulse and Momentum: mv1 + Fdt = mv2 , where
t1
r
mv1 : initial linear momentum of particle at time t1;
r
mv 2
Rectilinear Kinematics of a Particle
Definitions:
position coordinate s: choose origin and direction.
P
O
s
s
v
ds
dt
dv d 2 s
dt dt 2
dv dv ds
dv
v
or a
dt ds dt
ds
Relation between s, v, and a:
derivative
derivative
s
v
a
integration
integration
veloci
Exam II Review
Chapter 15 Kinetics of a Particle: Impulse and Momentum
r
r
Liner momentum of a particle: L = mv . It is a vector.
t2 r
r
r
Principle of Linear Impulse and Momentum: mv1 + Fdt = mv2 , where
t1
r
mv1 : initial linear momentum of particle at
Exam I Review
Chapter 12 Kinematics of a Particle
Rectilinear Motion of Particles
position coordinate s: choose origin and direction.
P
O
s
s
v=
velocity:
acceleration:
ds
dt
or
dv d 2 s
=
dt dt 2
dv dv ds
dv
=
=v
a=
dt ds dt
ds
a=
Two important rectiline
Impact
1.
In the case of central impact, two colliding bodies A and B move along the line of impact with
velocities (vA)1 and (vB)1 , respectively. Two equations can be used to determine their velocities
(vA)2 and (vB)2 after the impact. The first repres