The sound source of a ship’s sonar system operates at a frequency of 22.0 kHz . The speed of sound in water (assumed to be at a
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Answer:
3.4 x 10⁴ m/s
Explanation:
Analyze the circular path of the electron
B = magnetic field = 80 x 10⁻⁶ T
m = mass of an electron = 9.1 x 10⁻³¹ kg
v = speed in the radial direction
r = radius of the circular trajectory = 2 mm = 0.002 m
q = charge of an electron = 1.6 x 10⁻¹⁹ C
For the electron’s circular movement
qBr = mv
(1.6 x 10⁻¹⁹) (80 x 10⁻⁶) (0.002) = (9.1 x 10⁻³¹) v
v = 2.8 x 10⁴ m/s
Now, consider the electron's movement in a straight line:
v' = speed in linear motion
x = distance traveled horizontally = 9 mm = 0.009 m
t = duration = =
= 4.5 x 10⁻⁷ sec
Using the formula
x = v' t
0.009 = v' (4.5 x 10⁻⁷)
v' = 20000 m/s
v' = 2 x 10⁴ m/s
The resultant speed is given by
V = sqrt(v² + v'²)
V = sqrt((2.8 x 10⁴)² + (2 x 10⁴)²)
v = 3.4 x 10⁴ m/s
Answer:
the time it takes after impact for the puck is 2.18 seconds
Explanation:
initially given information
mass = 30 g = 0.03 kg
diameter = 100 mm = 0.1 m
thickness = 0.1 mm = 1 × m
dynamic viscosity = 1.75 × Ns/m²
temperature of air = 15°C
to determine
time needed for the puck to reduce its speed by 10%
solution
we note that velocity changes from 0 to v
assuming initial velocity = v
therefore final velocity = 0.9v
implying a change in velocity is du = v
and clearance dy = h
shear stress acting on the surface is expressed as
= µ
therefore
= µ ............1
substituting the values
= 1.75 × ×
= 0.175 v
the area between the air and puck is given by
Area =
area =
area = 7.85 × m²
thus, the force on the puck can be represented as
Force = × area
force = 0.175 v × 7.85 ×
force = 1.374 × v
now applying Newton's second law
force = mass × acceleration
- force =
- 1.374 × v =
solving for t =
the time needed after impact for the puck is 2.18 seconds
Answer:
According to the guideline for kilometers, every three seconds between a lightning strike and the subsequent thunder indicates the distance to the flash in kilometers.
Explanation:
To calculate the speed of sound in meters per second, we need to utilize certain conversion factors. One mile corresponds to 5 seconds after witnessing the lightning. Furthermore, 1 mile comprises 5280 feet, and 1 foot is equivalent to 0.3048 meters. This information is sufficient to solve the issue. The conversion ratios can be set up like this:
Observe how the ratios are organized such that the units cancel out during calculations. One ratio has miles in the numerator while the other has them in the denominator, leading to cancellation. The same applies to the feet.
The question requires us to provide the answer to one significant figure, resulting in the speed of sound rounding to 300m/s.
For the second part, we will again utilize conversions. This time we will set our ratios in reverse and realize that there are 1000 meters in 1 kilometer, leading us to:
This signifies that for every 3.11 seconds, the distance to the lightning strike is 1 kilometer. Since this is a fabric of general knowledge, we round to the nearest whole number for simplicity, establishing the guideline:
According to the rule for kilometers, every three seconds between a lightning flash and the following thunder gives the distance to the flash in kilometers.