Kinetics of a particle - Phiphat Phruksarojanakun · Kinetics of a particle. Objectives ... The...
Transcript of Kinetics of a particle - Phiphat Phruksarojanakun · Kinetics of a particle. Objectives ... The...
Kinetics of a particle
Objectives
• To analyze the accelerated motion of a particle using the equation of motion with different coordinate systems.
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Newton’s Laws of Motions (1687)
First Law
A particle originally at rest, or moving in a straight line with a constant velocity, will remain in this state provided the particle is not subjected to an unbalanced force.
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Newton’s Laws of Motions (1687)
First Law
A particle originally at rest, or moving in a straight line with a constant velocity, will remain in this state provided the particle is not subjected to an unbalanced force.
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Newton’s Laws of Motions (1687)
Second Law
The unbalanced force acting on the particle is proportional to the time rate of change of the particle’s linear momentum.
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Newton’s Laws of Motions (1687)
Third Law
The mutual forces of action and reaction between two particles are equal, opposite, and collinear.
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Equation of MotionRectangular Coordinates
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amF
zz
yy
xx
maF
maF
maF
Procedure for Analysis
• Select the inertial coordinate system
• Draw FBD
• Establish direction and sense of acceleration
• Solve for unknowns
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Problem 13-12
• Determine the normal force the 10-kg crate A exerts on the smooth cart if the cart is given an acceleration of a = 2 m/s2 down the plane. Also, what is the acceleration of the crate?
(θ=30⁰)
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Problem 13-23
A force F = 150 N is applied to the cord.
Determine how high the 300-N (~ 30 kg)
block A rises in 2 s starting
from rest. Neglect the weight
of the pulleys and cord.
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Equation of MotionNormal and Tangential Coordinates
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bb
nn
tt
maF
maF
maF
Problem 13-67
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Determine the constant speed of the passengers on the amusement-park ride if it is observed that the supporting cables are directed at θ=30⁰ from the vertical. Each chair including its passenger has a mass of 80 kg. Also, what are the components of force in the n, t and b directions which the chair exerts on a 50-kg passenger during the motion?
Equation of MotionCylindrical Coordinates
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zz
rr
maF
maF
maF
Useful Formulas
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2 rrar rra 2 zaz
ddr
r
/tan
Problem 13-88
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The boy of mass 40-kg is sliding down the spiral slide at a constant speed such that his position, measured from the top of the chute, has components r=1.5 m, θ=0.7t rad, and z=-0.5t m, where t is in seconds. Determine the components of force Fr, Fθ and Fz
which the slide exerts on him at the instant t=2 s. Neglect the size of the boy.
Example 1
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A can C, having mass 0.5-kg, moves along a grooved horizontal slot. The slot is in a form of spiral defined by equation r = (0.1θ) m, where θis in radians. If the arm OA is rotating at a constant rate in the horizontal plane, determine the force it exerts on the can at the instant θ = π rad.