Chapter 13 – Oscillations and Waves Review Materials
Equations from the chapter:
2. A spring oriented vertically is attached to a hard horizontal surface as in Figure
P13.2. The spring has a force constant of 1.46 kN/m. How much is the spring
compressed when a object of mass m = 2.30 kg is placed on top of the spring and
the system is at rest? ( kN meam 1000 N)
The force compressing the spring is the weight of the object. Thus, the spring will be
compressed a distance of
8. A block of mass m = 2.00 kg is attached to a spring of force constant k =
5.00 X 102 N/m that lies on a horizontal frictionless surface as shown in Figure
P13.8. The block is pulled to a position x, = 5.00 cm to the right of equilibrium
and released from rest. Find (a) the work required to stretch the spring and
(b) the speed the block has as it passes through equilibrium.
(a)
The work required to stretch the spring equals the elastic potential energy of the spring in the stretched
condition, or
(b)
In the initial condition, the spring-block system is at rest
with elastic potential energy of
. Since the spring force is conservative, conservation of energy gives
. Thus, when the block is at the equilibrium position (
we have
),
, or
11. A child's toy consists of a piece of plastic attached to a spring (Fig. P13.11).
The spring is compressed against the floor a distance of 2.00 cm, and the toy is
released. If the toy has a mass of 100 g and rises to a maximum height of 60.0
cm, estimate the force constant of the spring.
(a) The work required to stretch the spring equals the elastic potential energy of
the spring in the stretched condition, or
(b)
In the initial condition, the spring-block system is at rest
with elastic potential
energy of
. Since the spring force is conservative, conservation of energy gives
. Thus, when the block is at the equilibrium position (
), we have
, or
19. At an outdoor market, a bunch of bananas attached to the bottom of a vertical spring of force
constant 16.0 N/m is set into oscillatory motion with an amplitude of 20.0 cm. It is observed that the
maximum speed of the bunch of bananas is 40.0 cm/s. What is the weight of the bananas in Newtons?
The maximum speed occurs at the equilibrium position and is
. Thus,
and
20. A 50.0-g object is attached to a horizontal spring with a force constant of 10.0 N/m and released
from rest with an amplitude of 25.0 cm. What is the velocity of the object when it is halfway to the
equilibrium position if the surface is frictionless?
34. A man enters a tall tower, needing to know its height. He notes that a long pendulum
extends from the ceiling almost to the floor and that its period is 15.5 s. (a) How tall is the
tower? (b) If this pendulum is taken to the Moon, where the free-fall acceleration is 1.67 m/s2,
what is the period there?
(a)
The height of the tower is almost the same as the length of the
pendulum. From
(b)
, we obtain
On the Moon, where
, the period will be
43.
Light waves are electromagnetic waves that travel at 3.00 X 108 m/s. The eye is most
sensitive to light having a wavelength of 5.50 X 10-7 m. Find (a) the frequency of this light wave
and (b) its period.
(a)
wavelength,
(b)
The speed of propagation for a wave is the product of its frequency and its
. Thus, the frequency must be
The period is
44.
The distance between two successive minima of a transverse wave is 2.76 m. Five crests
of the wave pass a given point along the direction of travel every 14.0 s. Find (a) the frequency
of the wave and (b) the wave speed.
(a)
The frequency of a transverse wave is the number of crests that pass a given
point each second. Thus, if 5.00 crests pass in 14.0 seconds, the frequency is
(b)
The wavelength of the wave is the distance between successive maxima or
successive minima. Thus,
and the wave speed is
53. Transverse waves with a speed of 50.0 m/s are to be produced on a stretched string. A
5.00-m length of string with a total mass of 0.060 0 kg is used. (a) What is the required tension
in the string?
(a)
The mass per unit length is
From
, the required tension in the string is
Tension is a FORCE!!