Answer:
21.21 N @ 81.87°
Explanation:
Divide each force into horizontal components and vertical components.
F₁ is in the +x direction, so F₁ₓ = 12 N and F₁ᵧ = 0 N.
F₂ is in the +y direction, so F₂ₓ = 0 N and F₂ᵧ = 9 N.
F₃ is 53.13° above the -x axis. So the components are:
F₃ₓ = -15 cos (53.13°) = -9 N
F₃ᵧ = 15 sin (53.13°) = 12 N
The horizontal component of the resultant force is the sum of the horizontal components of the individual forces:
Fₓ = F₁ₓ + F₂ₓ + F₃ₓ
Fₓ = 12 N + 0 N + (-9 N)
Fₓ = 3 N
Similarly, the vertical component of the resultant force is the sum of the vertical components of the individual forces:
Fᵧ = F₁ᵧ + F₂ᵧ + F₃ᵧ
Fᵧ = 0 N + 9 N + 12 N
Fᵧ = 21 N
To find the magnitude of the resultant force, use Pythagorean theorem:
F² = Fₓ² + Fᵧ²
F² = (3 N)² + (21 N)²
F = 21.21 N
To find the direction relative to the +x axis, use trigonometry:
tan θ = Fᵧ / Fₓ
tan θ = (21 N) / (3 N)
θ = 81.87°
The resultant force is 21.21 N at a angle of 81.87° above the +x axis (round as needed).
Answer:
t=2s
Explanation:
The definition of power is:
And the work-energy theorem states that:
Since the movement starts from rest, we have that:
And putting all together:
Since we want the time taken:
Which for our values is:
Answer: The five general characteristics of the nearest stars are the brightness, color, surface temperature, size, and mass.
Explanation:
The mass of a star can be described as being measured with our sun at 1 solar mass. One star can equal the size of our sun. There is one star named, Rigel, that is bigger than the Earths sun. Each star will vary in its density.
The size of the star, as stated above, can be the size of our sun and sometimes larger. The size is measured by solar radii.
Stars vary in their temp. They range anywhere from -273.15 degrees Celsius to 50,000 K. The temp is based on the Kelvin scale.
The stars brightness are always based on luminosity and magnitude.
The stars colors will vary and is based on the temperature of the surface of the star. Some stars are red in color, white in color, and some even have a bluish color.
Answer:
Explanation:
- The radio waves have a fixed relationship between the propagation speed (the speed of light in vacuum), the frequency and the wavelength, as follows:
- v = c = λ*f
where c= speed of light in vacuum = 3*10⁸ m/s, λ = wavelength =
4.92*10⁷ m.
Solving for f, we get the frequency of the radio waves:
f = 6.1 Hz
- Now, from the Hooke's law, we know that the mass attached at the end of the spring oscillates with an angular frequency defined by a fixed relationship between the spring constant k and the mass m, as follows:
- Now, we know that there exists a fixed relationship between the angular frequency and the frequency, as follows:
- We also know that f in (2) is the same that we got for the radio waves, so replacing (2) in (1), and rearranging terms, we can solve for k, as follows:
<span>Potassium carbonate (K2C03) is white salt and is often </span>found damp. It is soluble in water which makes a strong concoction. Hope this helps.
