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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