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lecture+notes+6 - 14:440:222 Dynamics (Lecture Note #6)...

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14:440:222 Dynamics (Lecture Note #6) Instructor: Prof. Peng Song Rutgers University Given: v A = 30 mi/h v B = 20 mi/h a B = 1200 mi/h 2 a A = 0 mi/h 2 Find: v B/A a B/A Plan: Write the velocity and acceleration vectors for A and B and determine v B/A and a B/A by using vector equations. Solution: The velocity of B is: v B = –20 sin(30) i + 20 cos(30) j = (–10 i + 17.32 j ) mi/h Solution to Example 4 from Lecture Note #5
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The velocity of A is: v A = –30 i (mi/h) The relative velocity of B with respect to A is ( v B/A ): v B/A = v B v A = (–10 i + 17.32 j ) – (–30 i ) = (20 i + 17.32 j ) mi/h or v B/A = (20) 2 + (17.32) 2 = 26.5 mi/h θ = tan -1 ( ) = 40.9° θ 17.32 20 Example 4 (cont’d) The acceleration of A is zero : a A = 0 The relative acceleration of B with respect to A is: a B/A = a B a A = 554.7 i +1706 j (mi/h 2 ) a A/B = (554.7) 2 + (1706) 2 = 1790 mi/h 2 β = tan -1 (1706 / 554.7) = 72° The acceleration of B is: a B = ( a t ) B + ( a n ) B = [– 1200 sin(30) i +1200 cos(30) j ] + [ ( ) cos(30) i +( ) sin(30) j ] a B = 554.7 i +1706 j (mi/h 2 ) 20 2 0.3 20 2 0.3 Example 4 (cont’d)
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Today’s Lecture • Newton’s second law of motion • Kinetics of particle systems The motion of an object depends on the forces acting on it. Newton’s Laws: Applications
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Newton’s Laws of Motion The motion of a particle is governed by Newton’s three laws of motion. First Law: A particle originally at rest, or moving in a straight line at constant velocity, will remain in this state if the resultant force acting on the particle is zero. Second Law: If the resultant force on the particle is not zero, the particle experiences an acceleration in the same direction as the resultant force. This acceleration has a magnitude proportional to the resultant force. Third Law: Mutual forces of action and reaction between two particles are equal, opposite, and collinear. The first and third laws were used in developing the concepts of statics. Newton’s second law forms the basis of the study of dynamics. Mathematically, Newton’s second law of motion can be written F = m a where F is the resultant unbalanced force acting on the particle, and a is the acceleration of the particle. The positive scalar m is called the mass of the particle. Newton’s second law cannot be used when the particle’s speed approaches the speed of light, or if the size of the particle is extremely small (~ size of an atom). Newton’s Laws of Motion (cont’d)
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Newton’s Law of Gravitational Attraction F = G(m 1 m 2 /r 2 ) where F = force of attraction between the two bodies, G = universal constant of gravitation , m 1 , m 2 = mass of each body, and r = distance between centers of the two bodies. When near the surface of the earth, the only gravitational force having
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lecture+notes+6 - 14:440:222 Dynamics (Lecture Note #6)...

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