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vova2212 [387]
3 years ago
8

A cat dozes on a stationary merry-go-round, at a radius of 5.5 m from the center of the ride. Then the operator turns on the rid

e and brings it up to its proper turning rate of one complete rotation every 6.3 s. What is the least coefficient of static friction between the cat and the merry-go-round that will allow the cat to stay in place, without sliding
Physics
1 answer:
bixtya [17]3 years ago
6 0

Answer:

u_{s}=0.56

Explanation:

For the cat to stay in place on the merry go round without sliding the magnitude of maximum static friction must be equal to magnitude of centripetal force

F_{s.max}=\frac{mv^2}{r} \\

Where the r is the radius of merry-go-round and v is the tangential speed

but

F_{s.max}=u_{s}F_{N}=u_{s}mg

So we have

u_{s}mg=\frac{mv^2}{r}\\ u_{s}=\frac{v^2}{gr}\\ Where\\v=\frac{2\pi R}{T} \\So\\u_{s}=\frac{(\frac{2\pi R}{T} )^2}{gr} \\u_{s}=\frac{4\pi^2 r}{gT^2}

Substitute the given values

So

u_{s}=\frac{4\pi^2 5.5m}{(9.8m/s^2)(6.3s)^2} \\u_{s}=0.56

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• reactants:

N = 2<em>a</em>, H = 4<em>a</em>, O = 3<em>a</em>

• products

N = 2<em>b</em>, O = 2<em>c</em> + <em>d</em>, H = 2<em>d</em>

<em />

Now we solve the system of equations,

2<em>a</em> = 2<em>b</em> … … … [1]

4<em>a</em> = 2<em>d</em> … … … [2]

3<em>a</em> = 2<em>c</em> + <em>d</em> … … … [3]

<em />

From [1] we immediately have

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In [2], we get

2<em>a</em> = <em>d</em>

and substituting for <em>d</em> in [3] gives

3<em>a</em> = 2<em>c</em> + 2<em>a</em>

<em>a</em> = 2<em>c</em>

<em />

Let <em>c</em> = 1; then

• <em>a</em> = 2×1 = 2

• <em>b</em> = 2

• <em>d</em> = 2×2 = 4

So, the balanced reaction is

2 NH₄NO₃   ⇒   2 N₂ + O₂ + 4 H₂O

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