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3 years ago

14

Calculate (a) the maximum capillary rise of water between two vertical glassplates spaced 0.15 mm apart and (b) the minimum capi

llary drop if the sameplates, now spaced 0.20 mm apart, are in mercury. Assume room temperature.

1 answer:

miss Akunina [59]3 years ago

5 0

Answer:

The the maximum capillary rise of water between two vertical glass plates is 9.79 cm

The the maximum capillary rise of mercury between two vertical glass plates is -2.77 cm

Explanation:

Given that,

Distance = 0.15 mm

Suppose, The surface tension of water is 72 dynes/cm at 25°C for pure water and perfectly clean glass, the angle of contact is 0°.

(a). We need to calculate the maximum capillary rise of water between two vertical glass plates

Using formula of rise of liquid in capillary tube

$h=\dfrac{2S\cos\theta}{r\rho g}$

Put the value into the formula

$h=\dfrac{2\times72\cos0}{0.015\times1\times980}$

$h=9.79\ cm$

(b). If the same plates, now spaced 0.20 mm apart, are in mercury

The density of mercury is 13.6 g/cm³, the angle of contact of mercury with glass is 139°, and the surface tension of mercury is 490 dyne/cm and g = 980 cm/s².

We need to calculate the minimum capillary drop

$h=\dfrac{2\times490\cos(139)}{0.02\times13.6\times980}$

$h=-2.77\ cm$

Hence, The the maximum capillary rise of water between two vertical glass plates is 9.79 cm

The the maximum capillary rise of mercury between two vertical glass plates is -2.77 cm

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The average speed of the ant is 0.276 cm/s and the average velocity is 0.136 cm/s.

The correct answer is option D.

In the given graph, we can deduce the following;

the total time of the motion, = 1 mins + 45 s = 60 s + 45 s = 105 s

The average speed of the ant is calculated as;

$average \ speed = \frac{total \ distance }{total \ time }$

The total distance from the graph is calculated as follows;

first horizontal distance from 2 cm to 8 cm = 8 - 2 = 6 cm

first upward distance from 3 cm to 5 cm = 5 - 3 = 2 cm

second horizontal distance from 8 cm to 6 cm = 8 - 6 = 2 cm

second upward distance from 5 cm to 12 cm = 12 - 5 = 7 cm

third horizontal distance from 6 cm to 13 cm = 13 - 6 = 7 cm

fourth downward distance from 12 cm to 9 cm = 3 cm

final horizontal distance from 13 cm to 15 cm = 2cm

The total distance = (6 + 2 + 2 + 7 + 7 + 3 + 2) cm = 29 cm

$average \ speed = \frac{total \ distance }{total \ time } = \frac{29 \ cm}{105 \ s} = 0.276 \ cm/s$

The average velocity is calculated as the change in displacement per change in time.

The displacement is the shortest distance between the start and end positions.

This shortest distance is the straight line connecting the start and end position. Call this line P

From the end position at x = 15 cm, draw a vertical line from y = 9 cm, to y = 3 cm. The displacement = 9 cm - 3 cm = 6 cm

Also, draw a horizontal line from start at x = 2 cm to x = 15 cm. The displacement = 15 cm - 2 cm = 13 cm

Notice, you have a right triangle, now calculate the length of line P.

↓end

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↓ 6cm

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start -------------13 cm------------

Use Pythagoras theorem to solve for P.

$P^2 = 6^2 + 13^2\\\\P^2 = 36 + 169\\\\P^2 = 205\\\\P= \sqrt{205} \\\\P = 14.318 \ cm$

The average velocity of the ant is calculated as;

$average \ velocity= \frac{\Delta displacemnt }{total\ time }= \frac{14.318 \ cm}{105 \ s} = 0.136 \ cm/s \\\\$

Thus, the average speed of the ant is 0.276 cm/s and the average velocity is 0.136 cm/s.

Learn more here: brainly.com/question/589950

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2 years ago

KE=0.5.m.v2 or PE=m.g.h

LUCKY_DIMON [66]

Answer:

1. 37.8J

2. 18 Billion Joules, 18 Gigajoules

3. 9.81 Billion Joules, 9.81 Gigajoules

Explanation:

Use the formulas provided,

KE=(1/2)mv^2 and PE=mgh, noting that g=9.81

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2 years ago

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The ball would have landed 3.31m farther if the downward angle were 6.0° instead.

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We can see in the picture that the least the angle the farther the ball will go. So we need to find the A and B position to determine how farther the second shot would go. Let's start with point A.

So, first we need to determine the components of the velocity of the ball, like this:

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$V_{Ax}=(21m/s)cos(-14^{o})$

$V_{Ax}=20.38 m/s$

$V_{Ay}=V_{A}sin\theta$

$V_{Ay}=(21m/s)sin(-14^{o})$

$V_{Ay}=-5.08 m/s$

we pick the positive one, so it takes 0.317s for the ball to hit on point A.

so now we can find the distance from the net to point A with this time. We can find it like this:

$x_{A}=V_{Ax}t$

$x_{A}=(20.38m/s)(0.317s)$

$x_{A}=6.46m$

Once we found the distance between the net and point A, we can similarly find the distance between the net and point B:

$V_{Bx}=20.88 m/s$

$V_{By}=-2.195 m/s$

$y_{Bf}=y_{B0}+V_{0}t-\frac{1}{2}at^{2}$

$0=2.1m+(-2.195m/s)t-\frac{1}{2}(-9.8m/s^{2})t^{2}$

$-4.9t^{2}-2.195t+2.1=0$

$t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$

$t=\frac{-(-2.195)\pm\sqrt{(-2.195)^{2}-4(-4.9)(2.1)}}{2(-4.9)}$

t= -0.9159s or t=0.468s

we pick the positive one, so it takes 0.468s for the ball to hit on point B.

so now we can find the distance from the net to point B with this time. We can find it like this:

$x_{B}=V_{Bx}t$

$x_{B}=(20.88m/s)(0.468s)$

$x_{B}=9.77m$

So once we got the two distances we can now find the difference between them:

$x_{B}-x_{A}=9.77m-6.46m=3.31m$

so the ball would have landed 3.31m farther if the downward angle were 6.0° instead.

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