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AysviL [449]
3 years ago
9

A mass of 30.0 grams hangs at rest from the lower end of a long vertical spring. You add different amounts of additional mass ΔM

to the end of the spring and measure the increase in length Δl of the spring due to the additional mass. You plot your data in the form Δl (vertical axis) versus ΔM (horizontal axis). Plotted this way, your data lies very close to a straight line that has slope 0.0268 m/kg. What is the force constant k of the spring? Use g = 9.80 m/s2.
Physics
2 answers:
Y_Kistochka [10]3 years ago
6 0

Answer:

366N/m

Explanation:

According to Hooke's law:

F=-kx

avoiding the minus symbol and substituting the force to the gravitational force, we have:

m.g=k.x\\k=\frac{m.g}{x}=\frac{m}{x}*g\\k=\frac{1}{s}*g\\k=\frac{1}{0.0268m/kg}*9.80m/s^2\\\\k=366N/m

The spring constant is 366N/m

ra1l [238]3 years ago
3 0

Answer:

K = 373.13 N/m

Explanation:

The force of the spring is equals to:

Fe - m*g = 0     =>    Fe = m*g

Using Hook's law:

K*X = m*g    Solving for K:

K = m/X * g

In this equation, m/X is the inverse of the given slope. So, using this value we can calculate the spring's constant:

K = 10 / 0.0268 = 373.13N/m

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Answer:

\tau=3.96\ ksi

Explanation:

Given that

d= 1.5 in                      ( 1 in = 0.0254 m)

d= 0.0381 m

P= 75 hp                      ( 1 hp = 745.7 W)

P= 55927.5 W

N= 1800 rpm

We know that power P is given as

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T=Torque

N=Speed

55927.5=\dfrac{2\times \pi \times 1800\ T}{60}

T=296.85 N.m

The maximum shear stress is given as

\tau=\dfrac{16 T}{\pi d^3}

\tau=\dfrac{16\times 296.85}{\pi \times 0.0381^3}

\tau=27.35\ MPa

We know that 1 MPa =0.145 ksi

\tau=3.96\ ksi

3 0
3 years ago
Suppose that two point charges, each with a charge of +1.00 C, are separated by a distance of 1.0 m. If the distance between the
Aleksandr-060686 [28]

Given:

The magnitude of each charge is q1 = q2 = 1 C

The distance between them is r = 1 m

To find the force when distance is doubled.

Explanation:

The new distance is

\begin{gathered} r^{\prime}=\text{ 2r} \\ =2\times1 \\ =2\text{ }m \end{gathered}

The force can be calculated by the formula

F=k\frac{q1q2}{(r^{\prime})^2}

Here, k is the constant whose value is

k=9\times10^9\text{ N m}^2\text{ /C}^2

On substituting the values, the force will be

\begin{gathered} F=9\times10^9\times\frac{1\times1}{(2)^2} \\ =2.25\times10^9\text{ N} \end{gathered}

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1 year ago
A sample of a gas has a volume of 639 cm3 when the pressure is 75.9 kPa. What is the volume of the gas when the pressure is incr
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Answer:

388 cm^3

Explanation:

For this problem, we can use Boyle's law, which states that for a gas at constant temperature, the product between pressure and volume remains constant:

pV=const.

which can also be rewritten as

p_1 V_1 = p_2 V_2

In our case, we have:

p_1 = 75.9 kPa is the initial pressure

V_1 = 639 cm^3 is the initial volume

p_2 = 125 kPa is the final pressure

Solving for V2, we find the final volume:

v_2 = \frac{p_1 V_1}{p_2}=\frac{(75.9)(639)}{125}=388 cm^3

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3 years ago
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a cone is constructed by cutting a sector from a circular sheet of metal with radius . the cut sheet is then folded up and welde
Svet_ta [14]

The expression for the radius and height of the cone can be obtained from

the property of a function at the maximum point.

  • The \ radius, \ of \ the \ base \ of \ the \ cone \ is \ \sqrt{ \dfrac{3}{4}} \times radius \ of \ circular \ sheet \ metal
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Reasons:

The part used to form the cone = A sector of a circle

The length of the arc of the sector = The perimeter of the circle formed by the base of the cone.

Volume \ of \ a \ cone = \dfrac{1}{3} \cdot  \pi \cdot r^3 \cdot h

  • Volume \ of \ a \ cone, \, V = \dfrac{1}{3} \cdot  \pi \cdot r^3 \cdot \sqrt{(s^2- r^2)}

θ/360·2·π·s = 2·π·r

Where;

s = The radius of he circular sheet metal

h = s² - r²

  • \dfrac{dV}{dr} = \dfrac{d}{dr}  \left(\dfrac{1}{3} \cdot  \pi \cdot r^3 \cdot \sqrt{(s^2- r^2)}\right) = \dfrac{\pi \cdot (3 \cdot r^2 \cdot  s^2 - 4 \cdot r^4)}{\sqrt{(s^2- r^2)}} = 0

3·r²·s² - 4·r⁴ = 0

3·r²·s² = 4·r⁴

3·s² = 4·r²

\underline{\left  \right. The \ radius, \, r =\sqrt{ \dfrac{3}{4}} \cdot s}

\underline{The \ height, \, h =\sqrt{s^2 - \dfrac{3}{4}\cdot s^2} = \dfrac{s}{2}}}

Learn more here:

brainly.com/question/14466080

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