Chapter 5: Applications of Newton's Laws

Transcription

1 Chapter 5 Lecture Chapter 5: Applications of Newton's Laws

2 Goals for Chapter 5 To draw free-body diagrams, showing forces on an individual object. To solve for unknown quantities using Newton's 2 nd law on an object or objects connected to one another. To relate the force of friction acting on an object to the normal force exerted on an object in 2 nd law problems. To use Hooke's law to relate the magnitude of the spring force exerted by a spring to the distance from the equilibrium position the spring has been stretched or compressed.

3 The Conditions for a Particle to be in Equilibrium Necessary conditions for an object to settle into equilibrium: Or in component form: Note: an object in equilibrium may be at rest or moving with a constant velocity.

4 Equilibrium in One Dimension Figure 5.1 Follow Example 5.1 on page 123.

5 Two Dimensional Equilibrium Example 5.2 Both x- and y-forces must be considered separately. Follow Example 5.2 on page 124.

6 An Example Involving Two Systems Example 5.4 See the worked example on page 126. This example brings nearly every topic we have covered so far in the course. This is an equilibrium problem because system moves with constant speed!! Note: x-axis for the cart does not have to align with the horizontal direction and is different from the bucket.

7 Let's Examine Applications of Newton's Second Law. à Non-equilibrium or Dynamic Problems Although this container is on a level surface, the liquid surface is on a slant because the apparatus is being accelerated to the left.

8 Application I Example 5.5 This experiment works in your car, a bus, or even an amusement park ride!

9 Application II Example 5.6 This sled ride is worked out for you on page 129. Similar to Example 5.4, but now velocity is not constant

10 Application III Example 5.7 This problem involves two interactive systems in a common lab experiment.

11 Contact Force and Friction We need to re-examine problems we formerly did as "ideal." We need to be able to find frictional forces given the mass of the object and the nature of the surfaces in contact with each other. There are two regions of friction: 1) when an object is sliding with respect to a surface à kinetic-friction force 2) when there is no relative motion à static-friction force

12 The Microscopic View of Friction Figure 5.12 A surface will always have imperfections, your perception of them depends on the magnification. The coefficient of friction (µ) will reveal how much force is involved.

13 No Dependence on Surface Area The normal force determines friction.

14 Friction Changes as Forces Change Figure 5.13 Forces from static friction increase as force increases while forces from kinetic friction are relatively constant. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.

15 How Much Effort to Move the Crate? Dynamics as in the last chapter with a new force. See the worked solution on page 135.

16 Forces Applied at an Angle The previous example has one new step if the force is applied at an angle. Please refer to the worked example on page 136.

17 A Toboggan on a Steep Hill with Friction Example 5.12 Similar to Example 5.6, but now at constant speed.

18 Forces in Fluids Figure 5.20 This topic is fully developed in advanced courses. Conceptually, observe the drag as objects fall through "thicker" liquids.

19 Elastic Forces Springs or other elastic material will exert force when stretched or compressed. The magnitude of the spring force F spring is given by Hooke's Law: Where k is spring constant [N/m] and ΔL [m] is distance the spring is stretched or compressed from its equilibrium length.

20 Stretch a Spring to Weigh Objects Example 5.14 The force settings on the spring are calibrated with mass standards at normal earth gravity. The spring scales are often calibrated in force (N) and mass (kg).

21 There are a Variety of Force Laws in Nature Gravitational interactions Electromagnetic interactions Strong interaction Weak interactions A "holy grail" of physics is the unified field theory. The goal will be to find the overriding principles that give rise to each of these very similar phenomena.