PHYS 218 Chapter 4

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This chapter focuses on dynamics: the motion of objects and the forces that cause motion.

Forces

Interaction between two or more objects/bodies

Measured in Newtons (N) = kg m/s²

Usually an interaction that one body exerts on another
Vector quantity

Newton's Laws of Motion

All laws apply in Inertial Reference Frame (no acceleration acting on reference frame)

An object with no forces acting on it maintains a constant state of motion
Force = mass × acceleration
For every action force, there is an equal and opposite reaction force.

Mass vs. Weight

Weight is a vector force that is acted upon by gravity (measured in Newtons)

Mass is a scalar and an intrinsic property of an object.

Monday, February 14, 2011 (PHYS 218 Exam 1 Review)

Normal Forces

contact force between 2 surfaces that is perpendicular to the surfaces

1 pair per surface (action/reaction) because of Newton's 3rd law

origin on object being described pointing away from contact surface

Monday, February 21, 2011

Gravitational Force

(constant; on surface of a planet)

weight (downward force) is equal to the mass times the acceleration due to gravity: $w=mg$

Origin is at the center of gravity
If $g$ is constant and the mass distribution of the object (i.e. density) is homogenous, center of gravity is the geometrical center of the object

Tension in a Rope

A means of applying a force to something else

If rope is massless, then force is transferred perfectly

tension is uniform throughout rope

Pulleys

Change direction of tension; magnitude stays the same!

Frictional Forces

Contact force between two surfaces that is parallel to surface

Kinetic Friction Force

Move with respect to each other
Opposite direction of velocity
Magnitude is proportional to Normal force: $|F_{k}|=\mu _{k}|N|\,\!$
μ_k (coefficient of kinetic friction) is a constant that depends on the characteristics of the two surfaces.

Static Friction Force

Does not move with respect to each other (i.e. objects are not moving)
"Direction opposes movement you would have if friction force wasn't there to begin with"
Magnitude grows to oppose applied force (up to a certain maximum given by $|F_{s}|\leq \mu _{s}|N|\,\!$ )
μ_s (coefficient of static friction; generally $\mu _{s}\leq \mu _{k}$ )

Used in ABS to attempt to keep overall frictional forces at a maximum.

Example: Walking on earth

${\frac {F_{earth\ on\ you}}{m_{you}}}=a_{you}$

${\frac {F_{you\ on\ earth}}{m_{earth}}}=a_{earth}$

${\frac {-F_{earth\ on\ you}}{m_{earth}}}=a_{earth}$

${\frac {a_{you}m_{you}}{m_{earth}}}=a_{earth}$