Answer:
50 N
Explanation:
Let the force in the horizontal rope be F₁ and the force in the diagonal rope be F₂:
The total force in the horizontal and vertical directions must be zero, since the object is at rest and is not accelerating.
The horizontal component of the forces:
F₁ + F₂ = -40N + F₂ = 0
F₂ = 40N
The vertical component of the forces:
F₁ + F₂ - mg = 0 + F₂ - mg = 0
F₂ = mg
If I assume the gravitational constant g = 10 m/s²:
F₂ = (3 kg) * (10 m/s²) = 30N
Adding the horizontal and vertical components of the force F₂:
F₂ = √((40N)² + (30N)²) = 50N
Answer:
The ratio of the energy stored by spring #1 to that stored by spring #2 is 2:1
Explanation:
Let the weight that is hooked to two springs be w.
Spring#1:
Force constant= k
let x1 be the extension in spring#1
Therefore by balancing the forces, we get
Spring force= weight
⇒k·x1=w
⇒x1=w/k
Energy stored in a spring is given by 
where k is the force constant and x is the extension in spring.
Therefore Energy stored in spring#1 is, 
⇒
⇒
Spring #2:
Force constant= 2k
let x2 be the extension in spring#2
Therefore by balancing the forces, we get
Spring force= weight
⇒2k·x2=w
⇒x2=w/2k
Therefore Energy stored in spring#2 is, 
⇒
⇒
∴The ratio of the energy stored by spring #1 to that stored by spring #2 is 
2:1
The mass number is the total number of protons and neutrons within an atom and since we know that the unknown element has 6 neutrons, we can simply subtract the number of neutrons from the mass number to get the number of protons.
17 - 6 = 11
There are 11 protons in this unknown element.
Extra:
The number of protons (+) and electrons (-) are equal in a neutral atom so since you know that there are 11 protons you also know that there are 11 electrons. On the periodic table, the element with 11 electrons is Na or Sodium.
Hope this helps! :)
Answer:
Tp/Te = 2
Therefore, the orbital period of the planet is twice that of the earth's orbital period.
Explanation:
The orbital period of a planet around a star can be expressed mathematically as;
T = 2π√(r^3)/(Gm)
Where;
r = radius of orbit
G = gravitational constant
m = mass of the star
Given;
Let R represent radius of earth orbit and r the radius of planet orbit,
Let M represent the mass of sun and m the mass of the star.
r = 4R
m = 16M
For earth;
Te = 2π√(R^3)/(GM)
For planet;
Tp = 2π√(r^3)/(Gm)
Substituting the given values;
Tp = 2π√((4R)^3)/(16GM) = 2π√(64R^3)/(16GM)
Tp = 2π√(4R^3)/(GM)
Tp = 2 × 2π√(R^3)/(GM)
So,
Tp/Te = (2 × 2π√(R^3)/(GM))/( 2π√(R^3)/(GM))
Tp/Te = 2
Therefore, the orbital period of the planet is twice that of the earth's orbital period.
