Chapter 5 Lecture
Chapter 5: Applications of Newton's Laws
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Goals for Chapter 5
• To draw free-body diagrams, showing forces on an individual object.
• To solve for unknown quantities using Newton's 2nd 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 2nd 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.
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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.
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Equilibrium in One Dimension – Figure 5.1
• Follow Example 5.1 on page 123.
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Two Dimensional Equilibrium – Example 5.2
• Both x- and y-forces must be considered separately.
• Follow Example 5.2 on page 124.
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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.
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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.
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Application I – Example 5.5
• This experiment works in your car, a bus, or even an amusement park ride!
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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
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Application III – Example 5.7
• This problem involves two interactive systems in a common lab experiment.
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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
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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.
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No Dependence on Surface Area
• The normal force determines friction.
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Friction Changes as Forces Change – Figure 5.13 • Forces from static friction increase as force
increases while forces from kinetic friction are relatively constant.
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How Much Effort to Move the Crate?
• Dynamics as in the last chapter with a new force. • See the worked solution on page 135.
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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.
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A Toboggan on a Steep Hill with Friction – Example 5.12 • Similar to Example 5.6, but now at constant
speed.
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Forces in Fluids – Figure 5.20
• This topic is fully developed in advanced courses.
• Conceptually, observe the drag as objects fall through "thicker" liquids.
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Elastic Forces
• Springs or other elastic material will exert force when stretched or compressed.
• The magnitude of the spring force Fspring 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.
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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).
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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.
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