EGCE-202: Dynamics
Lecture 2
California State University Fullerton
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Contents
2 Kinematics of particle
2.1 Motion of several particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Dependent Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Relative motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Projectile motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Curvilinear motion of particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Kinematics of particle
2.1
Motion of several particles
2.1.1
Dependent Motion
• Motion of one particle depends on motion of another particle
• Problem constraint is used to relate the displacements
Example 2.1. In Figure 1, if the end of the cable at A is pulled down with a speed of 5 m/s, determine
the speed at which block B rises.
Figure 1: Block and pulley system
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2.1.2
Relative motion
• Motion of one particle with respect to another particle
• If xA and xB are absolute position of points A and B
• xB/A is relative position of B relative to A
• Then xB = xA + xB/A ; VB = VA + VB/A ; aB = aA + aB/A
Example 2.2. In Figure 2, if block A of the pulley system is moving downward at 6 f t/s while block C
is moving down at 18 f t/s, determine the relative velocity of block B with respect to C.
Figure 2: Block and pulley system
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Example 2.3. In Figure 3, In the position shown, collar B moves to the left with a constant velocity of
300 mm/s. Determine (a) the velocity of collar A, (b) the velocity of portion C of the cable, (c) the
relative velocity of portion C of the cable with respect to collar B.
Figure 3: Block and pulley system
2.2
Projectile motion
• Projectile motion can be treated as two rectilinear motions:
– horizontal direction experiencing zero acceleration
– vertical direction experiencing constant acceleration (i.e., from gravity)
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Figure 4: Projectile motion
Example 2.4. In Figure 5, a pump is located near the edge of the horizontal platform shown. The nozzle
at A discharges water with an initial velocity of 25 f t/s at an angle of 55◦ with the vertical. Determine
the range of values of the height h for which the water enters the opening BC.
Figure 5: Pump and platform system
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Example 2.5. In Figure 6, the catapult is used to launch a ball such that it strikes the wall of the building
at the maximum height of its trajectory. If it takes 1.5 s to travel from A to B, determine the velocity
vA at which it was launched, the angle of release θ, and the height h
Figure 6: Catapult system
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2.3
Curvilinear motion of particles
• Motion of particle along curved path
• Vectors are used to describe the motion
Figure 7: Curvilinear motion
• Position of particle : r(t)
• Displacement : ∆r = r0 − r
• Average Velocity : vavg = ∆r
∆t
• Instantaneous velocity : v = dr
dt
• The velocity vector, v, is always tangent to the path of motion.
• Acceleration represents the rate of change in the velocity of a particle
• Acceleration : a = dv
dt
x
• If r = xî + y ĵ + z k̂, ax = dv
dt = v̇x = ẍ
Example 2.6. Airplane B, which is traveling at a constant 800 km/h, is pursuing airplane A, which is
traveling northeast at a constant 560 km/hr. At time t = 0, airplane A is 640 km east of airplane B.
Determine (a) the direction of the course airplane B should follow (measured from the east) to intercept
plane A, (b) the rate at which the distance between the airplanes is decreasing, (c) how long it takes for
airplane B to catch airplane A.
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Example 2.7. In Figure 8, a particle travels along the circular path from A to B in 1 s. If it takes 3 s
for it to go from A to C, determine its average velocity when it goes from B to C
Figure 8: Circular path
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