Answer:
|A| = 8.06
Explanation:
Given that
Vector A,
We need to find the magnitude of the vector. Let the vector is R = ai + bj. The magnitude of this vector is given by :
In this given question, a = 4 and b = 7
The magnitude of vector A is given by :
|A| = 8.06
So, the magnitude of given vector is 8.06. Hence, this is the required solution.
Answer:
F = 4856.32 N
Explanation:
Given,
A satellite is orbiting earth at a distance from Earth surface, h = 35000 m
The mass of the satellite, m = 500 Kg
The radius of the Earth, R = 6.371 x 10⁶ m
The mass of the Earth, M = 5.972 x 10²⁴ Kg
The gravitational constant, G = 6.67408 x 10 ⁻¹¹ m³ kg⁻¹ s⁻²
The force between the Earth and the satellite is given by the formula
F = GMm/(R+h)² N
Substituting the values in the above equation
F = (6.67408 x 10 ⁻¹¹ X 5.972 x 10²⁴ X 500) / (6.371 x 10⁶ + 35000)²
= 4856.32 N
Hence, the force between the planet and the satellite is, F = 4856.32 N
The total work <em>W</em> done by the spring on the object as it pushes the object from 6 cm from equilibrium to 1.9 cm from equilibrium is
<em>W</em> = 1/2 (19.3 N/m) ((0.060 m)² - (0.019 m)²) ≈ 0.031 J
That is,
• the spring would perform 1/2 (19.3 N/m) (0.060 m)² ≈ 0.035 J by pushing the object from the 6 cm position to the equilibrium point
• the spring would perform 1/2 (19.3 N/m) (0.019 m)² ≈ 0.0035 J by pushing the object from the 1.9 cm position to equilbrium
so the work done in pushing the object from the 6 cm position to the 1.9 cm position is the difference between these.
By the work-energy theorem,
<em>W</em> = ∆<em>K</em> = <em>K</em>
where <em>K</em> is the kinetic energy of the object at the 1.9 cm position. Initial kinetic energy is zero because the object starts at rest. So
<em>W</em> = 1/2 <em>mv</em> ²
where <em>m</em> is the mass of the object and <em>v</em> is the speed you want to find. Solving for <em>v</em>, you get
<em>v</em> = √(2<em>W</em>/<em>m</em>) ≈ 0.46 m/s
Half-life<span> is defined as the time it takes for one-</span>half<span> of the atoms of a radioactive material to disintegrate. </span>Half-lives<span> for various </span>radioisotopes<span> can range from a few microseconds to billions of years.</span>