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2 years ago

What is the magnitude of the force acting on a spring with a spring constant of 275 N/m that is stretched 14.3 cm?

Physics

1 answer:

Travka [436]2 years ago

8 0

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A permeability test was run on a compacted sample of dirty sandy gravel. The sample was 175 mm long and the diameter of the mold

LUCKY_DIMON [66]

Answer:

(a). The coefficient of permeability is $8.6\times10^{-3}\ cm/s$ .

(b). The seepage velocity is 0.0330 cm/s.

(c). The discharge velocity during the test is 0.0187 cm/s.

Explanation:

Given that,

Length = 175 mm

Diameter = 175 mm

Time = 90 sec

Volume= 405 cm³

We need to calculate the discharge

Using formula of discharge

$Q=\dfrac{V}{t}$

Put the value into the formula

$Q=\dfrac{405}{90}$

$Q=4.5\ cm^3/s$

(a). We need to calculate the coefficient of permeability

Using formula of coefficient of permeability

$Q=kiA$

$k=\dfrac{Q}{iA}$

$k=\dfrac{Ql}{Ah}$

Where, Q=discharge

l = length

A = cross section area

h=constant head causing flow

Put the value into the formula

$k=\dfrac{4.5\times175\times10^{-1}}{\dfrac{\pi(175\times10^{-1})^2}{4}\times38}$

$k=8.6\times10^{-3}\ cm/s$

The coefficient of permeability is $8.6\times10^{-3}\ cm/s$ .

(c). We need to calculate the discharge velocity during the test

Using formula of discharge velocity

$v=ki$

$v=\dfrac{kh}{l}$

Put the value into the formula

$v=\dfrac{8.6\times10^{-3}\times38}{17.5}$

$v=0.0187\ cm/s$

The discharge velocity during the test is 0.0187 cm/s.

(b). We need to calculate the volume of solid in the ample

Using formula of volume

$V_{s}=\dfrac{M_{s}}{V_{s}}$

Put the value into the formula

$V_{s}=\dfrac{4950\times10^{-3}}{2710}$

$V_{s}=1826.56\ cm^3$

We need to calculate the volume of the soil specimen

Using formula of volume

$V=A\times L$

Put the value into the formula

$V=\dfrac{\pi(17.5)^2}{4}\times17.5$

$V=4209.24\ cm^3$

We need to calculate the volume of the voids

$V_{v}=V-V_{s}$

Put the value into the formula

$V_{v}=4209.24-1826.56$

$V_{v}=2382.68\ cm^3$

We need to calculate the seepage velocity

Using formula of velocity

$Av=A_{v}v_{s}$

$v_{s}=\dfrac{Av}{A_{v}}$

$v_{s}=\dfrac{V}{V_{v}}\times v$

Put the value into the formula

$v_{s}=\dfrac{4209.24}{2382.68}\times0.0187$

$v_{s}=0.0330\ cm/s$

The seepage velocity is 0.0330 cm/s.

Hence, (a). The coefficient of permeability is $8.6\times10^{-3}\ cm/s$ .

(b). The seepage velocity is 0.0330 cm/s.

(c). The discharge velocity during the test is 0.0187 cm/s.

8 0

2 years ago

A student solving for the acceleration of an object has applied appropriate physics principles and obtained the expression a = a

Nikitich [7]

Answer:

The correct option is option (a).

The acceleration of an object is $\frac{33}{7}$ m/s².

Explanation:

Given expression is

$a=a_1+\frac Fm$

[ divide a whole number by 1 to turn into a fraction. Since $a_1$ is a whole number, so $a_1$ is divided by 1 to turn into a fraction]

$\Rightarrow a=\frac{a_1}{1}+\frac Fm$

[The l.c.m of the denominators 1 and m is m. Now multiply both numerator and denominator by m of $\frac{a_1}1$ and multiply both numerator and denominator by 1 of $\frac Fm$ ]

$\Rightarrow a=(\frac mm\times\frac{a_1}{1})+(\frac 11\times\frac Fm)$

The correct option is option (a)

Given that,

F= 12.0 kg.m/s² , m=7.00 kg and $a_1$ = 3.00 m/s²

$\therefore a=(\frac mm\times\frac{a_1}{1})+(\frac 11\times\frac Fm)$

$=(\frac{7.00}{7.00}\times \frac{3.00}{1})+(\frac11\times \frac{12.0}{7.00})$

$=\frac{21}{7}+\frac{12}{7}$

$=\frac{21+12}{7}$

$=\frac{33}{7}$ m/s²

The acceleration of an object is $\frac{33}{7}$ m/s².

8 0

2 years ago

What factors affect the ability of a substance to transfer thermal energy to heat or be heated by it's surroundings?

xeze [42]

The prime factors that affect the ability of substances to transfer the thermal energy to heat are the temperature difference between the two objects, area of cross-section, time, and distance travelled by the thermal energy.

Explanation: 

The process of heat conduction takes place through contact between two or more objects. But this conduction depends on multiple factors that are responsible for thermal conduction. They are-

Temperature Difference( $\Delta T$ ) - The two objects must have a temperature difference else there will be no thermal conduction between them. The more the difference in their temperatures, the more thermal energy flows from one object to the other.
Area of Cross-section (A) - Larger areas of contact provide as better medium of thermal conduction.
Time (t) - The more time we give for the thermal conduction, the more energy is transmitted from one system to the other.
Distance Travelled (l) - The longer the distance, lesser the conduction. Means, the distance should be minimized in order to achieve the optimum thermal conduction between two objects.

Consider metal pot and its handle, it is being boiled for 15 m. The molecules present near the source of heat, showing fast vibration and bounce off. It actually indicates the heats of substance. That’s why, handle remains hot as heat conduction takes place. It can be estimated by,

$Q=\frac{k A \Delta T t}{l}$

k - Thermal conductivity of the material, measured in J/s.m. $^{\circ} \mathrm{C}$

4 0

2 years ago

A 1.0 kg block is attached to an unstretched

KonstantinChe [14]

Answer:

Change in potential energy of the block-spring-Earth

system between Figure 1 and Figure 2 = 1 Nm.

Explanation:

Here, spring constant, k = 50 N/m.

given block comes down eventually 0.2 m below.

here, g = 10 m/s.

let block be at a height h above the ground in figure 1.

⇒In figure 2, potential energy of the block-spring-Earth

system = m×g×(h - 0.2) + 1/2× k × x². where, x = change in spring length.

⇒ Change in potential energy of the block-spring-Earth

system between Figure 1 and Figure 2 = (m×g×(h - 0.2)) - (1/2× k × x²)

= (1×10×0.2) - (1/2×50×0.2×0.2) = 1 Nm.

4 0

2 years ago

How many turns should a 10-cm long solenoid have if it is to generate a 1.5 x 10-3 t magnetic field on 1.0 a of current?

stepan [7]

We can answer this problem using Ampere’s Law:

Bh = μoNI

Where:

B = Magnetic Field

h = coil length

μo = permeability =4π*10^-7 T·m/A

N = number of turns

I = current

It is given that B=0.0015T, I=1.0A, h=10 cm = 0.1m

Use Ampere's law to find # turns:
Which can be rewritten as:
N = Bh/μoI 
N = (0.0015)(0.1)/(4π*10^-7)(1.0)
N = 119.4

Answer: 119.4 turns

3 0

2 years ago