. Why are SI units helpful to scientists especially when describing objects?

An engineer is designing a runway. She knows that a plane, starting at rest, needs to reach a speed of 180mph at take-off. If th

kvv77 [185]

Answer:

The plane would need to travel at least $8,\!580\; {\rm ft}$ ( $8.58 \times 10^{3}\; {\rm ft}$ .)

The $10,\!000\; {\rm ft}$ runway should be sufficient.

Explanation:

Convert unit of the the take-off velocity of this plane to $\rm ft\cdot s^{-1}$ :

$\begin{aligned}v &= 180\; {\rm mph} \\ &= 180\; {\rm mi \cdot hrs^{-1}} \times \frac{1\; {\rm hrs}}{3600\; {\rm s}} \times \frac{5280\; {\rm ft}}{1\; {\rm mi}} \\ &= 264\; {\rm ft \cdot s^{-1}}\end{aligned}$ .

Initial velocity of the plane: $u = 0\; {\rm ft \cdot s^{-1}}$ .

Take-off velocity of the plane $v =264\; {\rm ft\cdot s^{-1}}$ .

Let $x$ denote the distance that the plane travelled along the runway. Since acceleration is constant but unknown, make use of the SUVAT equation $x = ((u + v) / 2) \, t$ .

Notice that this equation does not require the value of acceleration. Rather, this equation make use of the fact that the distance travelled (under constant acceleration) is equal to duration $t$ times average velocity $(u + v) / 2$ .

The distance that the plane need to cover would be:

$\begin{aligned}x &= \left(\frac{u + v}{2}\right)\, t \\ &= \frac{0\; {\rm ft \cdot s^{-1}} + 264\; {\rm ft \cdot s^{-1}}}{2} \times 65.0\; {\rm s} \\ &= 8.58\times 10^{3}\; {\rm ft}\end{aligned}$ .

4 0

3 years ago

Identify the palindromic base sequence in the DNA donor molecule shown.

Airida [17]

Explanation:

Since a double helix is formed by two paired antiparallel strands of nucleotides that run in opposite directions, and the nucleotides always pair in the same way (adenine (A) with thymine (T) in DNA or uracil (U) in RNA; cytosine (C) with guanine (G)), a (single-stranded) nucleotide sequence is said to be a palindrome

6 0

3 years ago

Which one of the following statements concerning superconductors is false? A constant current can be maintained in a superconduc

julsineya [31]

Answer:

All materials are superconducting at temperatures near absolute zero kelvin.

Explanation:

All materials are superconducting at temperatures near absolute zero kelvin is false concerning superconductors.

8 0

3 years ago

Estimate the smallest possible period of a satellite in a circular orbit around earth. (mass and radius of earth is 5.98 x 1024

myrzilka [38]

Given: Mass of earth Me = 5.98 x 10²⁴ Kg

Radius of earth r = 6.37 x 10⁶ m

G = 6.67 x 10⁻¹¹ N.m²/Kg²

Required: Smallest possible period T = ?

Formula: F = ma; F = GMeMsat/r² Centripetal acceleration ac = V²/r

but V = 2πr/T

equate T from all equation.

F = ma

GMeMsat/r² = Msat4π²/rT²

GMe = 4π²r³/T²

T² = 4π²r³/GMe

T² = 39.48(6.37 x 10⁶ m)³/6.67 x 10⁻¹¹ N.m²/Kg²)(5.98 x 10²⁴ Kg)

T² = 1.02 x 10²² m³/3.99 x 10¹⁴ m³/s²

T² = 25,563,909.77 s²

T = 5,056.08 seconds or around 1.4 Hour

3 0

3 years ago

A blow-dryer and a vacuum cleaner each operate with a voltage of 120 V. The current rating of the blow- dryer is 11 Amps, and th

AURORKA [14]

Answer:

(a) 1320 W

(b) 480 W

(c) E':E ≈ 11:2

Explanation:

(a) Applying,

P' = VI'................. Equation 1

Where P' = Power of the blow-dryer, V = Voltage, I = current rating of the blow-dryer.

From the question,

Given: V = 120 V, I' = 11 A

Substitute these values into equation 1

P = (120×11)

P = 1320 W

(b) Similarly,

P = VI................... Equation 2

Where P = Power of the vacuum cleaner. I = current rating of the vacuum cleaner.

Also Given: I = 4 A,

Therefore

P = 4(120)

P = 480 W

(c)

E' = P'/t'............. Equation 3

E = P/t................ Equation 4

Where E' = Energy of the blow-dryer, t' = time of use of the blow-dryer, E = Energy of the vacuum cleaner, t = time of use of the vacuum cleaner

From the question,

Given: t' = 15 minutes = (15×60) = 900 seconds, t = 30 minutes = (30×60) = 1800 seconds

Substitute these values into equation 3 and 4

E' = 1320/900

E' = 1.47 J,

E = 480/1800

E = 0.267

Therefore,

E':E = 1.47:0.267

E':E ≈ 11:2

5 0

3 years ago