Mae 208 dynamics dr matthew bryant note set 5 page 12

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MAE 208 Dynamics Dr. Matthew Bryant Note Set 5 Page 12 of 15 Analyzing Oblique Impacts When we have oblique impact, we get velocities with unknown directions and unknown magnitudes If we know initial velocities, this leaves us with four unknowns So how do we set the problem up? Establish the x-axis along the line of impact o Causes deformation and restitution to occur only in x Establish the y-axis along the plane of contact Write out four independent scalar equations to solve for the unknowns What are these four equations??
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MAE 208 Dynamics Dr. Matthew Bryant Note Set 5 Page 13 of 15 Example: The curling stone A slides over the ice and strikes another stone B as shown. If each stone is smooth and has a weight of 47 lb and the coefficient of restitution is e = 0.8 , determine their speeds just after collision. Initially, A has a velocity of 8 ft/s and B is at rest.
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MAE 208 Dynamics Dr. Matthew Bryant Note Set 5 Page 14 of 15 Example: A long fly ball strikes the wall at point A ( e 1 = 0.5) and then hits the ground at B ( e 2 = 0.3). The outfielder likes the catch the ball when it is 4 ft above the ground and 2 ft in front of him as shown. Determine the velocity vector of the ball after impacting the wall at A Find the velocity vector of the ball just before impact at B Find how far the ball has traveled in x to reach point B Determine the velocity vector of the ball after impacting the ground at B Determine the distance x from the wall where he can catch the ball as described ( hint: there are two possible solutions after the bounce at B )
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MAE 208 Dynamics Dr. Matthew Bryant Note Set 5 Page 15 of 15 Important Equations from this Note Set Principle of linear impulse and momentum 2 1 2 1 t t v m dt F v m or……. 2 1 2 1 2 1 2 1 2 1 2 1 ) ( ) ( ) ( ) ( ) ( ) ( t t z z t t y y t t x x v m dt F v m v m dt F v m v m dt F v m Conservation of linear momentum 2 1 ) ( ) ( i i i i v m v m Coefficient of restitution 1 1 2 2 B A A B v v v v e Central impact 2 2 1 1 B B A A B B A A v m v m v m v m Oblique impact 2 2 1 1 Bx B Ax A Bx B Ax A v m v m v m v m 1 1 2 2 Bx Ax Ax Bx v v v v e 2 1 Ay A Ay A v m v m 2 1 By B By B v m v m
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  • Spring '08
  • Silverberg
  • Force, Momentum, linear impulse, impulsive forces, Dr. Matthew Bryant

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