Akg object and a kg object are separated by m. find the magnitude of the net gravitational force exerted by these objects on a kg object placed midway between them. at what position other than an infinitely remote one can the kg object be placed so as to experience a net force of zero from the other two objects?

F₂ = 0 N

x = 0.5*d = 0.5 m

Explanation:

Given

m₁ = m₂ = m₃ = m = 1 Kg

d = distance between m₁ and m₃ = d₁₃ = 1 m

d₁₂ = 0.5*d = 0.5*(1 m) = 0.5 m = d₃₂

G = 6.673*10⁻¹¹ N*m²/ Kg²

a) Find the magnitude of the net gravitational force exerted by these objects on a kg object (F₃) placed midway between them.

we can apply

F₂ = F₁₂ + F₃₂

then we use the formula

F₁₂ = G*m₁*m₂ / d₁₂² = G*m² / (0.5*d)² = 4*G*m² / d²

⇒ F₁₂ = 4*G*m² / d² = 4*(6.673*10⁻¹¹ N*m²/ Kg²)*(1 Kg)² / (1 m)²

⇒ F₁₂ = 2.6692*10⁻¹⁰ N (←)

and

F₃₂ = G*m₃*m₂ / d₃₂² = G*m² / (0.5*d)² = 4*G*m² / d²

⇒ F₃₂ = 4*G*m² / d² = 4*(6.673*10⁻¹¹ N*m²/ Kg²)*(1 Kg)² / (1 m)²

⇒ F₃₂ = 2.6692*10⁻¹⁰ N (→)

we get

F₂ = F₁₂ + F₃₂ = (- 2.6692*10⁻¹⁰ N) + (2.6692*10⁻¹⁰ N) = 0 N

b) At what position other than an infinitely remote one can the kg object be placed so as to experience a net force of zero from the other two objects?

From a) It is known that x = 0.5*d = 0.5*(1 m) = 0.5 m

Nevertheless, we can find the distance as follows

If

F₂ = 0   ⇒   F₁₂ + F₃₂ = 0   ⇒   F₁₂ = - F₃₂

If

x = distance between m₁ and m₂

d - x = distance between m₂ and m₃

we get

F₁₂ = G*m² / x²

F₃₂ = G*m² / (d - x)²

If   F₁₂ = - F₃₂

⇒     G*m² / x² = - G*m² / (d - x)²

⇒     1 / x² = - 1 / (d - x)²  

⇒    (d - x)² = - x²

⇒  d²- 2*d*x + x² = - x²

⇒  2*x² - 2*d*x + d² = 0

⇒  2*x² - 2*1*x + 1² = 0

⇒  2*x² - 2*x + 1 = 0

Solving the equation we obtain

x = 0.5 m = 0.5*d

explanation:

earth's surface is mainly heated by the absorption of infrared radiation from the sun.

evaporation occurs because molecules in liquid water are warmed ( usually by the sun) and vibrate quicker, becoming less dense and rise.

condensation occurs because molecules in water vapor are cooled and therefore vibrate more slowly thus becoming more dense and eventually fall to earth.

lines of equal barometric pressure on a weather map are called: isobars : lines of equal temp on a weather map are called: isotherms.​

thermal energy is the answer