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aliina [53]
3 years ago
14

Determine the force of gravitational attraction between the earth (m = 5.98 x 10^24kg)

Physics
1 answer:
yKpoI14uk [10]3 years ago
7 0

Answer:

F = 683.8 N

Explanation:

The gravitational force of attraction between the Earth and the student is given by Newton's Law of Gravitation as follows:

F = \frac{Gm_{1}m_{2}}{r^2}

where,

F = Force = ?

G = Universal gravitational constant = 6.67 x 10⁻¹¹ Nm²/kg²

m₁ = mass of Earth = 5.98 x 10²⁴ kg

m₂ = mass of student = 70 kg

r = distance between Earth and student = 6.39 x 10⁶ m

Therefore,

F = \frac{(6.67\ x\ 10^{-11}\ Nm^2/kg^1)(5.98\ x\ 10^{24}\ kg)(70\ kg)}{(6.39\ x\ 10^6\ m)^2}\\

<u>F = 683.8 N</u>

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A hot-water stream at 80 ℃ enters a mixing chamber with a mass flow rate of 0.5 kg/s where it is mixed with a stream of cold wat
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\dot{m_1}= 0.5kg/s

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T₁ = 80⁰C ⇒ h₁ = 335.02 kJ/kg

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T₃ = 42⁰C ⇒ h₃ = 175.90 kJ/kg

we know

\dot{m_{in}}=\dot{m_{out}}

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according to energy balance equation

\dot{m_{in}}h_{in}=\dot{m_{out}}h_{out}

\dot{m_{1}}h_{1}+\dot{m_{2}}h_{2}=\dot{m_{3}}h_{3}

\dot{m_{1}}h_{1}+\dot{m_{2}}h_{2}=(\dot{m_{1}}+\dot{m_{2}})h_{3}\\(0.5\times 335.02)+(\dot{m_{2}}\times 83.915)=(0.5+\dot{m_{2}})175.90\\\dot{m_{2}}=0.865 kg/s

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Why could the beam of particles not have a neutral charge?
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Two forces, F₁ and F₂, act at a point. F₁ has a magnitude of 8.00 N and is directed at an angle of 61.0° above the negative x ax
kirill115 [55]

1) -7.14 N

2) +2.70 N

3) 7.63 N

Explanation:

1)

In order to find the x-component of the resultant force, we have to resolve each force along the x-axis.

The first force is 8.00 N and is directed at an angle of 61.0° above the negative x axis in the second quadrant: this means that the angle with respect to the positive x axis is

180^{\circ}-61^{\circ}

so its x-component is

F_{1x}=(8.00)(cos (180^{\circ}-61^{\circ}))=-3.88 N

F₂ has a magnitude of 5.40 N and is directed at an angle of 52.8° below the negative x axis in the third quadrant: so, its angle with respect to the positive x-axis is

180^{\circ}+52.8^{\circ}

Therefore its x-component is

F_{2x}=(5.40)(cos (180^{\circ}+52.8^{\circ}))=-3.26 N

So, the x-component of the resultant force is

F_x=F_{1x}+F_{2x}=-3.88+(-3.26)=-7.14 N

2)

In order to find the y-component of the resultant force, we have to resolve each force along the y-axis.

The first force is 8.00 N and is directed at an angle of 61.0° above the negative x axis in the second quadrant: as we said previously, the angle with respect to the positive x axis is

180^{\circ}-61^{\circ}

so its y-component is

F_{1y}=(8.00)(sin (180^{\circ}-61^{\circ}))=7.00 N

F₂ has a magnitude of 5.40 N and is directed at an angle of 52.8° below the negative x axis in the third quadrant: as we said previously, its angle with respect to the positive x-axis is

180^{\circ}+52.8^{\circ}

Therefore its y-component is

F_{2y}=(5.40)(sin (180^{\circ}+52.8^{\circ}))=-4.30 N

So, the y-component of the resultant force is

F_y=F_{1y}+F_{2y}=7.00+(-4.30)=2.70 N

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The two components of the resultant force representent the sides of a right triangle, of which the resultant force corresponds tot he hypothenuse.

Therefore, we can find the magnitude of the resultant force by using Pythagorean's theorem:

F=\sqrt{F_x^2+F_y^2}

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F_x=-7.14 N is the x-component

F_y=2.70 N is the y-component

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F=\sqrt{(-7.14)^2+(2.70)^2}=7.63 N

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