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3 years ago

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Estimate how fast your hair grows, in units of m/s, assuming it takes 30 days for your hair to grow 1 inch. note that 1 inch =2.

54cm
2. how many liters (L) of water does it take to fill a swimming pool that is 15.0 feet long, 15.0 feet wide, and 8.00 feet deep? first compute the volume of the swimming pool in ft^3 and then follow the unit conversion rules to convert the units to L. note that 1ft=0.3048 meter and 1 L =1000cm^3

1 answer:

dedylja [7]3 years ago

6 0

Answer:

1) 9.8×10⁻⁹ m/s

2) 50970.3238656 L

Explanation:

1) In 30 days hair grows 1 inch

1 inch = 2.54 cm

1 cm = 0.01 m

2.54 cm = 2.54 × 0.01 m

⇒2.54 cm = 0.0254 m

30 days = 30×24×60×60 = 2592000 seconds

Speed = Distance / Time

$\text{Speed}=\frac{0.0254}{2592000}=9.8\times 10^{-9}\ m/s$

Speed at which hair grows is 9.8×10⁻⁹ m/s

2) 1 ft = 0.3048 m

0.3048 m = 30.48 cm

1 ft = 30.48 cm

15 ft = 15×30.48 = 457.2 cm

8 ft = 8×30.48 = 243.84 cm

Volume of water in pool = Length × Width × Depth

⇒Volume of water in pool = 457.2×457.2×243.84

⇒Volume of water in pool = 50970323.8656 cm³

or

Volume of water in pool = 15×15×8 = 1800 ft³

1 ft³ = 30.48³ cm³

1800 ft³ = 30.48³ × 1800 = 50970323.8656 cm³

Converting to liters

1 L = 1000 cm³

0.001 L = 1 cm³

50970323.8656 cm³ = 50970323.8656×0.001 = 50970.3238656 L

Volume of water in pool is 50970.3238656 L

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A charge of 32.0 nC is placed in a uniform electric field that is directed vertically upward and has a magnitude of 4.30x 104 V/

hodyreva [135]

A) The work done by the electric field is zero

B) The work done by the electric field is $9.1\cdot 10^{-4} J$

C) The work done by the electric field is $-2.4\cdot 10^{-3} J$

Explanation:

A)

The electric field applies a force on the charged particle: the direction of the force is the same as that of the electric field (for a positive charge).

The work done by a force is given by the equation

$W=Fd cos \theta$

where

F is the magnitude of the force

d is the displacement of the particle

$\theta$ is the angle between the direction of the force and the direction of the displacement

In this problem, we have:

The force is directed vertically upward (because the field is directed vertically upward)
The charge moves to the right, so its displacement is to the right

This means that force and displacement are perpendicular to each other, so

$\theta=90^{\circ}$

and $cos 90^{\circ}=0$ : therefore, the work done on the charge by the electric field is zero.

B)

In this case, the charge move upward (same direction as the electric field), so

$\theta=0^{\circ}$

and

$cos 0^{\circ}=1$

Therefore, the work done by the electric force is

$W=Fd$

and we have:

$F=qE$ is the magnitude of the electric force. Since

$E=4.30\cdot 10^4 V/m$ is the magnitude of the electric field

$q=32.0 nC = 32.0\cdot 10^{-9}C$ is the charge

The electric force is

$F=(32.0\cdot 10^{-9})(4.30\cdot 10^4)=1.38\cdot 10^{-3} N$

The displacement of the particle is

d = 0.660 m

Therefore, the work done is

$W=Fd=(1.38\cdot 10^{-3})(0.660)=9.1\cdot 10^{-4} J$

C)

In this case, the angle between the direction of the field (upward) and the displacement (45.0° downward from the horizontal) is

$\theta=90^{\circ}+45^{\circ}=135^{\circ}$

Moreover, we have:

$F=1.38\cdot 10^{-3} N$ (electric force calculated in part b)

While the displacement of the charge is

d = 2.50 m

Therefore, we can now calculate the work done by the electric force:

$W=Fdcos \theta = (1.38\cdot 10^{-3})(2.50)(cos 135.0^{\circ})=-2.4\cdot 10^{-3} J$

And the work is negative because the electric force is opposite direction to the displacement of the charge.

Learn more about work and electric force:

brainly.com/question/6763771

brainly.com/question/6443626

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3 years ago

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Explanation:

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3 years ago

A ball rolls from 10 m to -25 m in 2.5 seconds. What was<br> its average velocity?<br> (Units = m/s)

marissa [1.9K]

Answer:

v = -14 m/s

Explanation:

Given that,

Initial location of the ball, X₁ = 10 m

Final position of the ball, X₂ = -25 m

Time taken to travel is, t = 2.5 s

The average velocity of the ball is given by the formula,

V = X₂ - X₁ / t m/s

Substituting the values in the above equation,

V = -25 - 10 / 2.5

= -14 m/s

The negative sign in the velocity indicates that ball rolls in the opposite direction.

Hence, the average velocity of the ball is v = -14 m/s

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3 years ago

Suppose that placing 0.3 inch of lead in front of a gamma source reduces the count rate from 1045 cps to 573 cps. What is um^-1

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Answer:

14.49 g/cm²

Explanation:

I = Io e^-(ux)

Where:

I = 573

Io = 1045

x = 0.3 inches and

rho = 11.4g/cm^3

Using the conversion constant

1 inch = 2.54 cm;

0.3 inches = 0.3 * 2.54 cm

0.3 inches = 0.762 cm

I/Io = e^-(ux), or say

Io/I = e^(ux), taking the In of both sides

ln(Io/I) = ux, making u subject of formula

u = 1/x * ln(Io/I)

u = 1/0.762 * ln(1045/573)

u = 1.312 * 0.6

u = 0.787

Next, we say that

u/rho = 0.7872/11.4 = 0.069

And finally, we make

1/(u/rho) to be our final answer

Inverse of the answer is = 14.49 g/cm²

Therefore, the um^-1 in g/cm^2? is 14.49

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3 years ago