Quiz

elastic head-on collision between two particles: (a) before collision and

(b) after collision.

across a horizontal surface with an initial speed v. It

slides until it stops due to the friction force between the block and the surface. The same block is now projected across the horizontal surface with an initial speed 2v. When the block has come to rest, how does the distance from the projection point compare to that in the first case? (a) It is the same. (b) It is twice as large. (c) It is four times as large. (d) The relationship cannot be determined.

Quick Quiz 2 A car and a large truck traveling at the same speed make a head-on collision and stick together. Which vehicle experiences the larger change in the magnitude of momentum? (a) the car (b) the truck (c) The change in the magnitude of momentum is the same for both. (d) impossible to determine.

object returns to a given position after a fixed time

interval. With a little thought, we can identify several types of periodic motion in everyday life. Your car returns to the driveway each afternoon. You return to the dinner table each night to eat. A bumped chandelier swings back and forth, returning to the same position at a regular rate. The Earth returns to the same position in its orbit around the Sun each year, resulting in the variation among the four seasons. The Moon returns to the same relationship with the Earth and the Sun, resulting in a full Moon approximately once a month.

when the force acting on an object is proportional to

the position of the object relative to some equilibrium position. If this force is always directed toward the equilibrium position, the motion is called simple harmonic motion.

block attached to a spring moving on a frictionless surface.

(a) When the block is displaced to the right of equilibrium (x > 0), the force exerted by the spring acts to the left. (b) When the block is at its equilibrium position (x = 0), the force exerted by the spring is zero. (c) When the block is displaced to the left of equilibrium (x < 0), the force exerted by the spring acts to the right.

(4.25)

Hooke’s law, a restoring force

(4.26)

An object moves with simple harmonic motion whenever its acceleration

is proportional to its position and is oppositely directed to the displacement from equilibrium.

(4.27)

motion, is simply the maximum value of the position of

the particle in either the positive or negative x direction. The constant ω is called the angular frequency, and has units of rad/s.

(4.35)

(or initial phase angle) and, along with the amplitude A,

is determined uniquely by the position and velocity of the particle at t = 0.

The quantity (ωt+φ) is called the phase of the motion.

demonstrating simple harmonic motion. A pen attached to the oscillating

object traces out a sinusoidal pattern on the moving chart paper.

is the time interval required for the particle to go

through one full cycle of its motion

called the frequency f of the motion. Whereas the period

is the time interval per oscillation, the frequency represents the number of oscillations that the particle undergoes per unit time interval:

The units of f are cycles per second, or hertz (Hz). Rearranging Equation 8.11 gives

(4.37)

(4.38)

depend only on the mass of the particle and the

force constant of the spring, and not on the parameters of the motion, such as A or φ.

(b) Velocity versus time. (c) Acceleration versus time. Note that

at any specified time the velocity is 90° out of phase with the position and the acceleration is 180° out of phase with the position.

periodic motion. It consists of a particle-like bob of mass

m suspended by a light string of length L that is fixed at the upper end, as shown in Figure 8.4.

simple pendulum depend only on the length of the string

and the acceleration due to gravity.

an object attached to a spring and submersed in a

viscous liquid.

In many real systems, nonconservative forces, such as friction, retard the motion. Consequently, the mechanical energy of the system diminishes in time, and the motion is said to be damped.

where b is a constant called the damping coefficient.

(4.50)

the retarding force is small, the oscillatory character of the

motion is preserved but the amplitude decreases in time, with the result that the motion ultimately ceases.

the velocity and the power transferred to the oscillator is

a maximum.

in the Tacoma Narrows Bridge, causing it to oscillate at

a frequency near one of the natural frequencies of the bridge structure. (b) Once established, this resonance condition led to the bridge’s collapse.

energy of a simple harmonic oscillator is a constant of

the motion and is proportional to the square of the amplitude.

(4.54)

disturbance,
a medium that can be disturbed, and
some physical

mechanism through which elements of the medium can influence each other.

the elements of the disturbed medium to move perpendicular to

the direction of propagation is called a transverse wave.

A traveling wave or pulse that causes the elements of the medium to move parallel to the direction of propagation is called a longitudinal wave.

surface of deep water in which a wave is propagating

is a combination of transverse and longitudinal displacements, with the result that elements at the surface move in nearly circular paths. Each element is displaced both horizontally and vertically from its equilibrium position.

who steps back and accidentally stomps on your foot with

the heel of one shoe. Would you be better off if that person were (a) a large professional basketball player wearing sneakers (b) a petite woman wearing spike-heeled shoes?

Quick Quiz 4.2 A grandfather clock depends on the period of a pendulum to keep correct time. Suppose a grandfather clock is calibrated correctly and then a mischievous child slides the bob of the pendulum downward on the oscillating rod. Does the grandfather clock run (a) slow (b) fast (c) correctly?