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Solnce55 [7]
2 years ago
12

A balloon of diameter 20.0 cm is filled with helium gas at 30°C at 1.00 atm. How

Physics
1 answer:
bogdanovich [222]2 years ago
8 0

Answer:

N = 3.54 * 10²³ atoms

Explanation:

The formula to apply here is the idea gas law;

PV = nRT  where ;

P= pressure of the gas= 1.013 * 10⁵ Pa

V= volume of the gas = 4/3 * 3.14 *0.15³= 0.01414 m³

n= amount of a substance = ?

R= ideal gas constant= 8.314

T= temperature= 293 K

Applying the values to the formula;

PV = nRT

1.013 * 10⁵ * 0.01414 = n * 8.314*293

n= 1.013 * 10⁵ * 0.01414 / 8.314*293

n= 0.588 moles

1 mole = 6.022 * 10²⁷ atoms/ mole

0.588 moles = 0.588 * 6.022 * 10²⁷

N = 3.54 * 10²³ atoms

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Answer:

(a). The height of the cliff is 41.67 m.

(b). The maximum height of the ball is 41.67 m

(c). The ball's impact speed is 16.52 m/s.

Explanation:

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Speed = 33 m/s

Angle = 60°

Time = 3.0 sec

(a). We need to calculate the height of the cliff

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h=ut-\dfrac{1}{2}gt^2

h=(u\sin60)\times t-\dfrac{1}{2}gt^2

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h=41.6\ m

(b). We need to calculate the maximum height of the ball

Using formula of height

h_{max}=\dfrac{(u\sin\theta)^2}{2g}

Put the value into the formula

h=\dfrac{(33\sin60)^2}{2\times 9.8}

h=41.67\ m

(c). We need to calculate the vertical component of velocity of ball

Using equation of motion

v=u-gt

v=u\sin\theta-gt

Put the value into the formula

v_{y}=33\times\sin 60-9.8\times3.0

v_{y}=-0.82\ m/s

We need to calculate the horizontal component of velocity of ball

Using formula of velocity

v_{x}=u\cos\theta

Put the value into the formula

v_{x}=33\times\cos60

v_{x}=16.5\ m/s

We need to calculate the ball's impact speed

Using formula of velocity

v=\sqrt{v_{x}^2+v_{y}^2}

Put the value into the formula

v=\sqrt{(16.5)^2+(-0.82)^2}

v=16.52\ m/s

Hence, (a). The height of the cliff is 41.67 m.

(b). The maximum height of the ball is 41.67 m

(c). The ball's impact speed is 16.52 m/s.

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