1. Chapter 13 Dynamics

2. Chapter 3 Newton’s Law

3. NEWTON'S LAW OF INERTIA A body, not acted on by any force, remains in uniform motion. NEWTON'S LAW OF MOTION Moving an object with twice the mass will require twice the force. Force is proportional to the mass of an object and to the acceleration (the change in velocity). F=ma.

5. W = m*g

6. Fnet = F = T1 + T2 + T3 = 0

7. x- and y-components: T1x = - T1 cos 37o = - 0.8 T1 T1y = T1 sin 37o = 0.6 T1 T2x = T2 cos 53o = 0.6 T2 T2y = T2 sin 53o = 0.8 T2

8. Solve for tension T1 and T2. Fnet,x = F x = T1 x + T2 x + T3 x = 0 T1 x + T2 x + T3 x = 0 - 0.8 T1 + 0.6 T2 + 0 = 0 T1 = 0.75 T2

9. Dynamics M1: up as positive: F net = T - m 1 *g = m 1 a1 M2: down as positive. F net = F = m 2 *g - T = m 2 a2 3. Constraint equation: a1 = a2 = a

10. Equations From previous: T - m 1 *g = m 1 a  T = m 1 g + m 1 a Previous for Mass 2: m 2 *g - T = m 2 a Insert above expr. for T m 2 g - ( m 1 g + m 1 a ) = m 2 a ( m2 - m1 ) g = ( m1 + m2 ) a ( m1 + m2 ) a = ( m2 - m1 ) g a = ( m 2 - m 1 ) g / ( m 1 + m 2 )

11. Rules 1. Free-Body Analysis, one for each mass + Newton’s Law 3. Algebra: Solve system of equations for all unknowns 2. Constraint equation(s): Define connections. You should have as many equations as Unknowns. COUNT!

12. M*g M*g*sin  -M*g*cos  j Mass m rests on the 30 deg. Incline as shown. Step 1: Free-Body Analysis. Best approach: use coordinates tangential and normal to the path of motion as shown.

13. Mass m rests on the 30 deg. Incline as shown. Step 1: Free-Body Analysis. Step 2: Apply Newton’s Law in each Direction: M*g M*g*sin  -M*g*cos  j N

14. Friction F =  k *N: Another horizontal reaction is added in negative x-direction. M*g M*g*sin  -M*g*cos  j N  k *N

15. Midterm 1 : Some suggestions Systematic work: it takes practice, lots of it. Passive understanding is good, yet you still must train yourself through active practice. It’s all mathematical: Practice calculus and analytical geometry!

16. Midterm 1: Suggestions cont’d ‘Deep Thinking 1’: Map the solution path BEFORE starting the analysis. ‘Deep Thinking 2’: Select the laws you will use. ‘Deep Thinking 3’: Map out the Connections between the laws that will lead to the answer.

17. Preparing for Exam 1 Modeling: Free-Body Analysis Laws and Definitions: Laws of Kinematics, Terms such as , Coriolis accel, Moving Frames of Ref. Seek to understand the concepts Practice problem solving. Copying the homework gives you an illusion and useless points

18. Multiple Masses A and B move in i and j-directions. Steps: 1.Write Newton for each Mass. 2.Constraint equation connects both masses. Here: vA = - vB

19. fig_03_007 Newton’s Law for Rotation

27. Step 1: Free-Body Analysis

28. Step 2: Newton in radial and tangential directions

29. Rotation Kinematics Similar to translation: and