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3 years ago

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A child's first bicycle has 12-inch tires. These tires have a 6-inch radius. How fa r does the bicycle move forward each time th

e wheel makes one complete rotation? Give your answer in meters. (1 inch = 0.022 meters) b. A woman's ten-speed bicycle has 27-inch tires (13.5-inch radius). How far does this bicycle …

1 answer:

Lilit [14]3 years ago

3 0

Answer:

a. s = 0.96 m

b. s = 2.15 m

Explanation:

a.

The relationship between the linear displacement and the angular displacement is given as follows:

$s = r\theta$

where,

s = linear distance covered = ?

r = radius of wheel = (6 in)(0.0254 m/1 in) = 0.1524 m

θ = angular displacement = (1 rev)(2π rad/1 rev) = 2π rad

Therefore,

$s = (0.1524\ m) 2\pi$

<u>s = 0.96 m</u>

<u></u>

b.

Assuming, we have to find linear displacement here, as well:

$s = r\theta$

where,

s = linear distance covered = ?

r = radius of wheel = (13.5 in)(0.0254 m/1 in) = 0.3429 m

θ = angular displacement = (1 rev)(2π rad/1 rev) = 2π rad

Therefore,

$s = (0.3429 \ m) 2\pi$

<u>s = 2.15 m</u>

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Both values from the question come with 3 significant figures. Keep more significant figures than that during the calculation and round the final result to the same number of significant figures.

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A sample of n2 gas occupies a volume of 746 ml at stp. What volume would n2 gas occupy at 155 ◦c at a pressure of 368 torr?

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Answer:

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We can solve the problem by using the ideal gas equation, which can be rewritten as:

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where we have:

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$V_1 = 746 mL = 0.746 L = 7.46\cdot 10^{-4}m^3$ is the initial volume

$T_1 = 0^{\circ}=273 K$ is the initial temperature (stp temperature)

$p_2 = 368 torr = 4.9\cdot 10^4 Pa$ is the final pressure

$V_2 = ?$ is the final volume

$T=155^{\circ}=428 K$ is the final temperature

By substituting the numbers inside the formula and solving for V2, we find the final volume:

$V_2 = \frac{p_1 V_1 T_2}{T_1 p_2}=\frac{(1.01\cdot 10^5 Pa)(7.46\cdot 10^{-4} m^3)(428 K)}{(273 K)(4.9\cdot 10^4 Pa)}=2.41\cdot 10^{-3} m^3$

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