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Review Session for CE2120-001

Review Session for CE2120-001. Dr. Zhang Feb. 26, 2014. Rectangular components Tangential & normal components Radial and transverse components. Overview. Position, Velocity & Acceleration. Physics  Mechanics  . Forces. Motion. Conservative forces (work independent of path) Gravity

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Review Session for CE2120-001

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  1. Review Session forCE2120-001 Dr. Zhang Feb. 26, 2014

  2. Rectangular components • Tangential & normal components • Radial and transverse components Overview Position, Velocity & Acceleration • Physics  Mechanics  • Forces • Motion • Conservative forces(work independent of path) • Gravity • Spring force • Gravitational force • Impulse forces (short time integral) • Linear momentum • Angular momentum

  3. Motion • Forces (Velocity) Overview (cont.) • Conservation of linear momentum • Conservation of angular momentum Impulse-Momentum (Velocities and time) (Forces and time) Work-Energy (Velocities and displacements) (Forces and displacements) Conservation of Energy Coefficient of Restitution

  4. Typical Problems Length of the rope = constant • Pulley system • Projectile • Collar • Slope & Spring & Pendulum constant (one degree of freedom) Gravity force Conservation of energy (a)y = - 9.81 m/s2 (a)x = 0 m/s2 • Gravity force • Spring force • Conservation of energy

  5. Typical Problems (cont.) • Conservation of angular momentum • Conservation of energy • Satellite • Impact Direct Central Impact Oblique Central Impact • Conservation of linear momentum • Coefficient of restitution [0 , 1]

  6. Typical Problems (cont.) • Conservation of angular momentum • Conservation of energy • Combinations

  7. Sample Problem 1 • SOLUTION: • This is a multiple step problem. Formulate your overall approach. • Use work-energy to find the velocity of the block just before impact A 2-kg block A is pushed up against a spring compressing it a distance x= 0.1 m. The block is then released from rest and slides down the 20º incline until it strikes a 1-kg sphere B, which is suspended from a 1 m inextensible rope. The spring constant k=800 N/m, the coefficient of friction between A and the ground is 0.2, the distance A slides from the unstretched length of the spring d=1.5 m, and the coefficient of restitution between A and B is 0.8. When a=40o, find (a) the speed of B (b) the tension in the rope. • Use conservation of momentum to determine the speed of ball B after the impact • Use work energy to find the velocity at a • Use Newton’s 2nd Law to find tension in the rope

  8. Sample Problem 1 (cont.) Given: mA= 2-kg mB= 1-kg, k= 800 N/m, mA =0.2, e= 0.8 Find (a) vB(b) Trope • Use work-energy to find the velocity of the block just before impact Determine the friction force acting on the block A Solve for N Sum forces in the y-direction

  9. Sample Problem 1 (cont.) Set your datum, use work-energy to determine vA at impact. 1 2 Determine values for each term. Datum x d Substitute into the Work-Energy equation and solve for vA

  10. Sample Problem 1 (cont.) • Use conservation of momentum to determine the speed of ball B after the impact • Draw the impulse diagram Note that the ball is constrained to move only horizontally immediately after the impact. Apply conservation of momentum in the x direction Use the relative velocity/coefficient of restitution equation (1) (2) Solve (1) and (2) simultaneously

  11. Sample Problem 1 (cont.) • Use work energy to find the velocity at a Set datum, use Work-Energy to determine vB at a= 40o 2 Determine values for each term. Datum 1 Substitute into the Work-Energy equation and solve for vA

  12. Sample Problem 1 (cont.) • Use Newton’s 2nd Law to find tension in the rope • Draw your free-body and kinetic diagrams en et • Sum forces in the normal direction • Determine normal acceleration • Substitute and solve

  13. Sample Problem 1 (cont.) Concept Question Compare the following statement to the problem you just solved. If the coefficient of restitution is smaller than the 0.8 in the problem, the tension T will be… Smaller Bigger If the rope length is smaller than the 1 m in the problem, the tension T will be… If the mass of A is smaller than the 2 kg given in the problem, the tension T will be… Smaller Bigger If the coefficient of friction is smaller than 0.2 given in the problem, the tension T will be… Smaller Bigger Smaller Bigger

  14. Good luck!

  15. Recliner & Curvilinear Motion • Position, Velocity & Acceleration • Rectangular components • Tangential & normal components • Radial and transverse components

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