The definition of the period of a wave is the time that it takes for the wave to complete one cycle. As stated in the problem, the certain water wave completes one cycle in 2 seconds. From this information alone, we can conclude that the period of the wave is indeed, 2 seconds.
Answer: 0.258
Explanation:
The resistance 
of a wire is calculated by the following formula:
(1)
Where:
is the resistivity of the material the wire is made of. For aluminium is 
and for copper is 
is the length of the wire, which in the case of aluminium is 
, and in the case of copper is 
is the transversal area of the wire. In this case is a circumference for both wires, so we will use the formula of the area of the circumference:
(2) Where 
is the diameter of the circumference.
For aluminium wire the diameter is 
and for copper is 
So, in this problem we have two transversal areas:
<u>For aluminium:</u>
(3)
<u>For copper:</u>
(4)
Now we have to calculate the resistance for each wire:
<u>Aluminium wire:</u>
(5)
(6) Resistance of aluminium wire
<u>Copper wire:</u>
(6)
(7) Resistance of copper wire
At this point we are able to calculate the ratio of the resistance of both wires:
(8)
(9)
Finally:
This is the ratio
Answer:
<em>I must travel with a speed of 2.97 x 10^8 m/s</em>
Explanation:
Sine the spacecraft flies at the same speed in the to and fro distance of the journey, then the time taken will be 6 months plus 6 months
Time that elapses on the spacecraft = 1 year
On earth the people have advanced 120 yrs
According to relativity, the time contraction on the spacecraft is gotten from
= 
where
is the time that elapses on the spacecraft = 120 years
= time here on Earth = 1 year
is the ratio v/c
where
v is the speed of the spacecraft = ?
c is the speed of light = 3 x 10^8 m/s
substituting values, we have
120 = 1/
squaring both sides of the equation, we have
14400 = 1/
14400 - 14400
= 1
14400 - 1 = 14400
14399 = 14400
= 14399/14400 = 0.99
= 0.99
substitute β = v/c
v/c = 0.99
but c = 3 x 10^8 m/s
v = 0.99c = 0.99 x 3 x 10^8 = <em>2.97 x 10^8 m/s</em>
Answer:
ΔP.E = 6.48 x 10⁸ J
Explanation:
First we need to calculate the acceleration due to gravity on the surface of moon:
g = GM/R²
where,
g = acceleration due to gravity on the surface of moon = ?
G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²
M = Mass of moon = 7.36 x 10²² kg
R = Radius of Moon = 1740 km = 1.74 x 10⁶ m
Therefore,
g = (6.67 x 10⁻¹¹ N.m²/kg²)(7.36 x 10²² kg)/(1.74 x 10⁶ m)²
g = 2.82 m/s²
now the change in gravitational potential energy of rocket is calculated by:
ΔP.E = mgΔh
where,
ΔP.E = Change in Gravitational Potential Energy = ?
m = mass of rocket = 1090 kg
Δh = altitude = 211 km = 2.11 x 10⁵ m
Therefore,
ΔP.E = (1090 kg)(2.82 m/s²)(2.11 x 10⁵ m)
<u>ΔP.E = 6.48 x 10⁸ J</u>
