Chapter 6 Dynamics I In Chapter 6, we begin to look at actual dynamics problems mostly in 1D, but some in 2D. Everything that we ll do is based on Newton s Second Law (from our last class): Newton s Second Law: The acceleration of the body is: Once we know the acceleration, kinematics tells us how the object moves. In 1D, we ll work with the component equation: And the 1D kinematics equations:
(will always be the case until we get to chapter 12) (Draw, draw, draw... ) (The FBD must be correct!) Use in component form: (We ll see both types of problems.)
Equilibrium Problems There are two types of equilibrium problems that we ll see: For particles, both types of equilibrium mean: And, in 2D, we ll always apply this in component form:
Whiteboard Problem 6-1 The three ropes in the figure below are tied to a small, very light ring. Two of the ropes are anchored to the walls at right angles, and the third rope pulls as shown. a) Draw a complete Free Body Diagram of the ring. b) What are T 1 (LC) and T 2, the magnitudes of the tension forces in Ropes 1 and 2?
Real Static Equilibrium (For real objects) Static Equilibrium for objects that can t be represented as a particle is somewhat different: consider a pencil subject to the two forces: FBD: y x No, it will rotate with an angular acceleration. For real objects in equilibrium, you need the force components to be zero and the sum of the torques about any point to also be zero - don t worry now, we ll do this in Chapter 12.
Whiteboard Prob. 6-2 The forces shown in the FBD below act on a 2.0 kg object. What are the x and y components of the object s acceleration, i.e. a x and a y (LC)? 5.0 N y 60 o 2.0 N x 3.0 N
PhET Computer Exercise: Forces in 1D Using the group s computer, one of you log onto Masteringphysics and begin the exercise: Lab PhET Forces in 1D. Use the computer to complete the exercise, but record your answers on the sheet to hand in that s what will be graded. When you re done with the exercise, make sure your Group s name and all of your names are on it, and turn it in. Feel free to play with the simulation if you have time. If you like to play and experiment with these simulations, go to http://phet.colorado.edu/ There are lots and lots of neat simulations, and, in the words of John Belushi, it don t cost nothing.
(Again) (will always be the case until we get to chapter 12) (Draw, draw, draw... ) (The FBD must be correct!) Use in component form: (We ll see both types of problems.)
Types of forces that we ll encounter in problems 1. Weight, the long range force of gravity on an object. 2. Normal Force, Contact force between objects that touch; direction is perpendicular (i.e. normal) to the surface at the point of contact. Note: read section 6.3 carefully and make sure that you understand the difference between mass and weight. Also, what force does a bathroom scale measure? (Note: I disagree with your author here, weight is always just the gravitational force on an object) y FBD of the person: Is this really the weight? The scale measures the force of contact between the person and the scale, i.e. the normal force. If there is an acceleration or the surface is tilted, the normal force won t equal the weight.
Whiteboard Problem: 6-3 Zach, whose mass is 80 kg, is standing on a scale in an elevator descending at 10 m/s. The elevator takes 3.0 s to brake to a stop at the first floor. a. Sketch the problem and draw a free body diagram of Zach; what is the reading on the scale before the elevator starts braking? b. Using the same free body diagram; what is the reading on the scale while the elevator is braking? (LC)
More types of forces 3. Tension: force of contact transmitted between a rope, string, or chain on an object. FBD of the box: NO! or? The tension force is always away from the object. My Civil Engineering friends refer to this as: Newton s Fourth Law: You can t push on a rope.
Friction Forces We will consider three types of friction forces between objects. Remember that what we are using are models based on experiments; they are not exact. All three are contact forces between objects. Kinetic Friction: when there is motion. Static Friction: when there is no motion. Note: static friction is a variable force Also Note: the direction of the impending motion is the direction that the object would move if there was no friction.
More Friction forces Rolling Friction: when there is rolling motion, there is friction present, but it is different than for sliding. A rolling friction force is modeled like a kinetic friction force. The coefficient of rolling friction is always much less than that for sliding motion. We ll talk about fluid drag next time.
Whiteboard Problem: 6-4 Bonnie and Clyde are sliding a 300 kg bank safe across a rough floor to their getaway car. Clyde pushes from behind with 385 N of force while Bonnie pulls forward on a rope with 350 N of force. a) Sketch the problem and Draw a complete Free Body Diagram of the safe. a) If the safe slides with a constant speed, determine the safe s coefficient of kinetic friction on the floor. (LC)