Fall 2011 PHYS 172: Modern Mechanics Lecture 7 – Speed of Sound in a Solid, Buoyancy Read 4.9 – 4.13

A desk has a mass of 57.5 kilograms. If the coefficient of static friction between the desk and the floor is 0.92, what force must be used to move the desk from rest?

Once the desk above is in motion, what force must be used to keep it moving at a constant velocity if the coefficient of kinetic friction is ?

A 7 kg object with initial speed = 5 m/s takes 2 seconds to stop due to friction. What is the coefficient of kinetic friction?

Derivative form of the Momentum Principle The Momentum Principle The rate of the momentum change is equal to force Works only if force is constant during  t If force changes introduce instantaneous rate of change: The momentum principle

Newton’s Second Law Assume nonrelativistic case: (definition of acceleration) Newton’s second law Traditional form of 2 nd Newton’s law (Assume m = const) Newton’s original formulation: The rate of change of amount of body’s motion is proportional to force momentum Momentum principle is the second Newton’s law

Spring-mass system: horizontal 1. System: block 2. Apply momentum principle: x y z Equilibrium =0

Spring-mass system: Analytical solution Motion along x: p x = p nonrelativistic Differential equation:

Spring-mass system: Analytical solution Search solution in form: Angular frequency amplitude t

Spring-mass system: period and frequency A -A t Period T: T2T2T Frequency : Angular frequency: [radian/second] A [s] [s -1 ]  [Hz]

Static equilibrium x y System is at rest: Can predict s: (system never moves)

Spring-mass system: vertical x y Choose origin at equilibrium position s0s0 Apply momentum principle: The same equation and motion in the presence of gravity if you choose origin at equilibrium! Details: 4.14 (p. 167)

Speed of sound in solids Qualitatively: Larger , larger v Larger d, larger v Detailed derivation:Speed of sound in a solid