By the law of universal gravitation, the gravitational force <em>F</em> between the satellite (mass <em>m</em>) and planet (mass <em>M</em>) is
<em>F</em> = <em>G</em> <em>M</em> <em>m</em> / <em>R </em>²
where
<em>• G</em> = 6.67 × 10⁻¹¹ m³/(kg•s²) is the universal gravitation constant
• <em>R</em> = 2500 km + 5000 km = 7500 km is the distance between the satellite and the center of the planet
Solve for <em>M</em> :
<em>M</em> = <em>F R</em> ² / (<em>G</em> <em>m</em>)
<em>M</em> = ((3 × 10⁴ N) (75 × 10⁵ m)²) / (<em>G</em> (6 × 10³ kg))
<em>M</em> ≈ 2.8 × 10¹⁴ kg
Answer:
kinetic energy is directly proportional to the mass of the object and to the square of its velocity: K.E. = 1/2 m v2. If the mass has units of kilograms and the velocity of meters per second, the kinetic energy has units of kilograms-meters squared per second squared.
Explanation:
Answer:
a. 86.80 m
b. i. The mass of the bob
ii. The length of the pendulum
Explanation:
a. Determine the height of the smokestack.
Using T = 2π√(L/g) where T = period of pendulum = 18.7 s, L = length of pendulum = height of smokestack and g = acceleration due to gravity = 9.8 m/s².
So, making L subject of the formula, we have
T = 2π√(L/g)
T/2π = √(L/g)
squaring both sides, we have
(T/2π)² = L/g
L = (T/2π)²g
Substituting the values of the variables into the equation, we have
L = (T/2π)²g
L = (18.7 s/2π)²(9.8 m/s²)
L = (2.976 s)²(9.8 m/s²)
L = 8.857 s² × 9.8 m/s²
L = 86.796 m
L ≅ 86.80 m
b. What factors influence the period of a simple pendulum
The factors that influence the period of a simple pendulum are
i. The mass of the bob
ii. The length of the pendulum
Answer:
Shown from explanation.
Explanation:
The resonant frequency is related by the formula;
Fo= 1/2π√(K/M)
Where Fo is resonant frequency
M is mass
K is the spring constant
From the expression above;
When K is increased frequency would increases since frequency is directly proportional to spring constant.
Similarly when the mass is increased the frequency decreases since frequency is inversely proportional to the mass.
Amplitude is a property of a wave and so the frequency stays same.
Answer:
Explanation:
Given that,
The current flowing in the circuit, I = 3 A
The power of the battery, P = 25 W
We need to find the resistance of the battery. We know that the power of the battery is given by the formula as follows :
Put all the values to find R.
So, the resistance is equal to .