Answer:
v = 3.7 m/s
Explanation:
As the swing starts from rest, if we choose the lowest point of the trajectory to be the zero reference level for gravitational potential energy, and if we neglect air resistance, we can apply energy conservation as follows:
m. g. h = 1/2 m v²
The only unknown (let alone the speed) in the equation , is the height from which the swing is released.
At this point, the ropes make a 30⁰ angle with the vertical, so we can obtain the vertical length at this point as L cos 30⁰, appying simply cos definition.
As the height we are looking for is the difference respect from the vertical length L, we can simply write as follows:
h = L - Lcos 30⁰ = 5m -5m. 0.866 = 4.3 m
Replacing in the energy conservation equation, and solving for v, we get:
v = √2.g.(L-Lcos30⁰) = √2.9.8 m/s². 4.3 m =3.7 m/s
Answer:
Fe = 25.67 N
Fg = 2.0734 x 10^-35 N
Explanation:
r = 3 x 10^-15 m
G = 6.67 x 10^-11 Nm^2/kg^2
Mp = 1.6726231 x 10^-27 kg
Qp = 1.6021 x 10^-19 C
K = 9 x 10^9 Nm^2/C^2
The formula for the electrical force between the two protons is given by


Fe = 25.67 N
The formula for the gravitational force between the two protons is given by


Fg = 2.0734 x 10^-35 N
Answer:
Explanation:
we know that
s=vt here v is the speed and s is distance covered by the signals
given data
v=3*10^8
t=10 min we have to convert it into seconds
1 minute=60 seconds
so
10 minutes =10*60/1 =600 seconds
now putting the value of v and t we can find the value of s
s=vt
s=3*10^8*600
s=1.8*10^11m
i hope this will help you
Answer:
d) 0 V
Explanation:
It can be showed that the potential due to a point charge q, to a distance d from the charge, can be expressed as follows:

where k = 
As the potential is an scalar, and is linear with the charge, we can apply the superposition principle, which means that we can find the potential due to one of the charges, as if the other were not present.
By symmetry, all four charges are at the same distance from the center, so we can write the total potential, as follows:

where d, is the semi-diagonal of the square, that we can find applying Pythagorean theorem, as follows:

Replacing by the values in (1) we have:

which is equal to the option d).
To solve this problem we will apply the concepts related to centripetal acceleration, which will be the same - by balance - to the force of gravity on the body. To find this acceleration we must first find the orbital velocity through the Doppler formulas for the given periodic signals. In this way:

Here,
Orbital Velocity
Maximal Wavelength
Average Wavelength
c = Speed of light
Replacing with our values we have that,

<em>Note that the average signal is 3.000000m</em>

Now using the definition about centripetal acceleration we have,

Here,
v = Orbit Velocity
r = Radius of Orbit
Replacing with our values,



Applying Newton's equation for acceleration due to gravity,

Here,
G = Universal gravitational constant
M = Mass of the planet
r = Orbit
The acceleration due to gravity is the same as the previous centripetal acceleration by equilibrium, then rearranging to find the mass we have,



Therefore the mass of the planet is 