1. Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Sections 818, 819, 820, 821 Lecture 10

2. A faulty model rocket moves in the xy-plane (the positive y- direction is vertically upward). The rocket’s acceleration has components a x (t)=  t 2 and a y (t)=  -  t, where  =2.50 m/s 4,  =9.00 m/s 2, and  =1.40 m/s 3. At t=0 the rocket is at the origin and has velocity with and a)Calculate the velocity and position vectors as functions of time. b)What is the maximum height reached by the rocket? c) What is the horizontal displacement of the rocket when it returns to y=0?

4. Dynamics Connection between force and motion The concept of force gives us a quantitative description of the interaction between two bodies or between a body and its environment

5. Newton’s Laws 1st Law: A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration 2nd Law: The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object. 3rd Law: For every action there is an equal, but opposite reaction

6. 2 nd Law From experiments we know: 1.Force is a vector 2.The direction of acceleration vector is the same as the direction of the force vector 3.The magnitude of the force and acceleration are related by a constant which depends on number of blocks involved.

7. Newton’s second law The vector acceleration of an object is in the same direction as the vector force applied to the object and the magnitudes are related by a constant called the mass of the object.

8. Gravitational force Force exerted by a spring: Hooke’s law: If spring is stretched or compressed by some small amount it exerted a force which is linearly proportional to the amount of stretching or compressing. The constant of proportionality is called the spring constant - is deviation from the natural length Normal force

9. The force resisting the pull of the spring – friction There is some maximum value the friction force can achieve, and once we apply a force greater than this maximum there is a net force on the object, so it accelerates. The maximum of the force of friction varied linearly with the amount that the block pushes on the table.  - coefficient of friction, is the vertical force exerted by the block on the table The friction force only exists when there is another force trying to move an object

10. Kinetic Friction For kinetic friction, it turns out that the larger the Normal Force the larger the friction. We can write F Friction =  Kinetic N Here  is a constant Warning: –THIS IS NOT A VECTOR EQUATION!

11. A Recipe for Solving Problems 1.Sketch Isolate the body (only external forces but not forces that one part of the object exert on another part) 2. Write down 2 nd Newton’s law Choose a coordinate system Write 2 nd Newton’s law in component form: 3. Solve for acceleration

12.  Pulling Against Friction A box of mass m is on a surface with coefficient of kinetic friction . You pull with constant force F P at angle  The box does not leave the surface and moves to the right. 1.What is the magnitude of the acceleration? 2.What angle maximizes the acceleration?

13. H Coefficient of friction:  What is the normal force? What is the velocity of the block when it reaches the bottom?

14. Have a great day! Reading: Chapter 5,6 Hw: Chapter 6 problems and exercises