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Transcript
Kinetics are the Cause • Kinetics cause Kinematics (not vice versa) • Kinematics such as velocity describe the motion. • Kinetics such as force, tell us what produced the motion. • E.g., A force acting on a mass produces an acceleration, which results in a change in velocity, and thus a change in displacement. 5/22/2017 Dr. Sasho MacKenzie - HK 376 1 Newton’s Second Law Explored The acceleration of an object is proportional to the net force acting on it. The acceleration is also in the same direction as the force. 5/22/2017 Dr. Sasho MacKenzie - HK 376 2 F = ma • All the external forces acting on an object are summed using vector addition to give you a net force which has both a magnitude and direction. • This net force will accelerate the object in the direction of the net force, and with a magnitude inversely proportional to the object’s mass. 5/22/2017 Dr. Sasho MacKenzie - HK 376 3 What’s the acceleration of the mass? F2 F1 F3 F4 5/22/2017 Dr. Sasho MacKenzie - HK 376 4 Finding Net Force F2 Net Force: F F3 F3 F4 F1 F2 5/22/2017 F1 F4 Dr. Sasho MacKenzie - HK 376 5 Representing Net Force 5 kg Net Force: F 50 N CM a = 50 N = 10 m/s/s 5 kg The net external force will accelerate the object’s center of mass (CM). 5/22/2017 Dr. Sasho MacKenzie - HK 376 6 Vector Addition y Net Force or Resultant: FR 30 N 5 kg x 10 N 30 N 10 N FR = (302 + 102) = 31.6 N Tan = Opposite = 10 N = 0.33 Adjacent 30 N = Arctan (0.33) = 18.4 5/22/2017 a = Net Force/Mass a = 31.6 N / 5 kg = 6.3 m/s/s a = 6.3 m/s/s 18.4 Dr. Sasho MacKenzie - HK 376 7 Resolving Vectors into y Components 5 kg 30 30 50 N x 50 N Fy Fx Force Components Cos (30) = Adj = Fx Hyp 50 N Fx = Cos (30)*50 N = 43.3 N ax = Fx/m = 43.3 / 5 = 8.7 m/s/s Sin (30) = Opp = Fy Hyp 50 N Fy = Sin (30)*50 N = 25.0 N ay = Fy/m = 25.0 / 5 = 5.0 m/s/s 5/22/2017 Acceleration Components Dr. Sasho MacKenzie - HK 376 8 F = ma not always useful • F = ma, tells us the instantaneous acceleration when the net force acts. • For most practical situations in biomechanics, velocity has more meaning than acceleration. • Further, practitioners such as coaches are usually interested in the velocity after a net force has acted. 5/22/2017 Dr. Sasho MacKenzie - HK 376 9 Impulse • To determine the speed of a baseball pitch, or how high someone will jump, we are interested in the average force exerted while the hand is in contact with the ball or the feet are in contact with the ground. • The product of the average force and the time that it acts is called impulse. Impulse F t • A net force of 100 N acting for 2 s generates 200 Ns of impulse. 5/22/2017 Dr. Sasho MacKenzie - HK 376 10 Change in Momentum • The momentum of an object is the product of its mass and velocity. Momentum mv • Conveniently for biomechanists, the Impulse-Momentum relationship states that a net impulse equals a change in momentum. • This relationship is really just a revised (actually original) form of the 2nd Law. 5/22/2017 Dr. Sasho MacKenzie - HK 376 11 Newton’s nd 2 Law Revised F ma Multiply both side by t Ft mat Since v = at Ft m v Impulse 5/22/2017 Change in momentum Dr. Sasho MacKenzie - HK 376 12 Impulse = Ft = Fdt • Impulse is the area under the force time curve. • It is the sum of all the infinitely small areas • It is equal to the change of momentum of an object. Momentum = mass x velocity. • If the object’s mass remains constant, impulse changes the velocity of an object. 5/22/2017 Dr. Sasho MacKenzie - HK 376 13 Impulse: Force vs. Time Graph Force (N) Time (s) •Impulse = Fdt = F1t1 + F2t2 + F3 t3 + …… = mv Instantaneous Force 5/22/2017 Infinitely small time period Dr. Sasho MacKenzie - HK 376 14 How fast is the pitch? A pitcher wears a special glove which allows the force between his hand and the ball to be calculated at every instant during the delivery. From the force/time graph below, we can calculate the speed of a 0.2 kg ball. Area under curve = 7 Ns ΣFΔt= Impulse Impulse = 7 Ns 20 Force (N) Time (s) 0.5 Impulse = m (Vf – Vi), Since Vi was zero, Vf =Impulse / m = 7 / 0.2 = 35 m/s = 78.8 mph Dr. Sasho MacKenzie 15 Ball Example F = 490.5 N A 490.5 N net force acts vertically downward on a 50 kg wrecking ball for 2 s. 50 kg 1. What is the acceleration of the ball? 2. If the ball was initially at rest, what is the final velocity of the ball? These questions can be answered with both forms of Newton’s 2nd Law 5/22/2017 Dr. Sasho MacKenzie - HK 376 16