Answer:
b = 0.6487 kg / s
Explanation:
In an oscillatory motion, friction is proportional to speed,
fr = - b v
where b is the coefficient of friction
when solving the equation the angular velocity has the form
w² = k / m - (b / 2m)²
In this exercise we are given the angular velocity w = 1Hz, the mass of the body m = 0.1 kg, and the spring constant k = 5 N / m. Therefore we can disperse the coefficient of friction
let's call
w₀² = k / m
w² = w₀² - b² / 4m²
b² = (w₀² -w²) 4 m²
Let's find the angular velocities
w₀² = 5 / 0.1
w₀² = 50
w = 2π f
w = 2π 1
w = 6.2832 rad / s
we subtitute
b² = (50 - 6.2832²) 4 0.1²
b = √ 0.42086
b = 0.6487 kg / s
ANSWER

EXPLANATION
Since the body is in equilibrium, total upward forces must equal total downward force.
Also the net horizontal forces acting on the body must be zero.
We need to resolve
into vertical and horizontal components.
The horizontal component is
.
The vertical component is
.
Equating the up force to the downward forces gives,
.
This implies that,
.

Also the horizontal forces must be equal.
.
Dividing equation (1) by equation (2) gives,
.


.
Therefore the given angle that
must make with the horizontal is approximately 35° to the nearest degree.
Answer:
Part(a): The angular acceleration is
.
Part(b): The angular displacement is
.
Explanation:
Part(a):
If
be the initial angular speed, final angular speed and angular acceleration of the centrifuge respectively, then from rotational kinematic equation, we can write

where '
' is the time taken by the centrifuge to increase its angular speed.
Given,
,
and
. From equation (
), the angular acceleration is given by

Part(b):
Also the angular displacement (
) can be written as

The basic relationship between frequency and wavelength for light (which is an electromagnetic wave) is

where c is the speed of light, f the frequency and

the wavelength of the wave.
Using

and

, we can find the value of the frequency:
Answer:
45.8 cm
Explanation:
To solve this, we will use the formula
5 / x² = 7/(1 - x)²
5 / x² = 7 / (1 - 2x + x²)
5 / 7 = x² / (1 - 2x + x²)
x = 0.5 * (√(35) - 5) meters
x = 0.5 * (5.916 - 5)
x = 0.5 * (0.916)
x = 0.458 or x = 45.8