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2 years ago

8

A hydraulic lift raises a 2000 kg automobile when a 500 N force is applied to the smaller piston. If the smaller piston has an a

rea of 10 cm2 , what is the cross-sectional area of the larger piston

1 answer:

Inga [223]2 years ago

5 0

Answer:

The cross-sectional area of the larger piston is 392cm ^{2}[/tex]

Explanation:

To solve this problem we apply the following formula:

Pascal principle: F=P*A Formula (1)

F=Force applied to the piston

P: Pressure

A= Piston area

Nomenclature:

Fp= Force on the primary piston= 500N

W= car weight =m*g=2000kg*9.8m/s2= 19600N

Fs= Force on the secondary piston= W = 19600N

$Ap= Primary piston area=10cm^{2} =10*10^{-4}m^{2}$

As= Secondary piston area=?

The pressure acting on one side is transmitted to all the molecules of the liquid because the liquid is incompressible.

In the equation (1)

P=F/A

Pp=Ps

$\frac{Fp}{Ap} = \frac{Fs}{As}$

$As= \frac{Fs*Ap}{Fp}$

$As=\frac{19600*10*10^{-4} }{500}$

$As=0.0392m^{2} =0.0392*10^{4}cm^{2}$

$As=392cm ^{2}$

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Answer:

The moment (torque) is given by the following equation:

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Explanation:

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1 year ago

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2 years ago

The table shows information about four students who are running around a track. Which statement is supported by the information

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Answer:

<em>Correct option: Mohammed has less kinetic energy than Autumn.</em>

Explanation:

<u>Kinetic Energy</u>

Is the energy an object has due to its motion. If the object has a mass m and travels at a speed v, then the kinetic energy K is:

$\displaystyle K=\frac{1}{2}mv^2$

The information about four students includes their mass and velocity as follows:

Autumn has a mass of m1=50 kg and a velocity (magnitude) of v1=4 m/s, thus their kinetic energy is:

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Mohammed has a mass of m2=57 kg and a velocity (magnitude) of v2=3 m/s, thus their kinetic energy is:

$\displaystyle K_2=\frac{1}{2}57\cdot 3^2$

$K_2=256.5\ J$

Lexy has a mass of m3=53 kg and a velocity (magnitude) of v3=2 m/s, thus their kinetic energy is:

$\displaystyle K_3=\frac{1}{2}53\cdot 2^2$

$K_3=106\ J$

Chiang has a mass of m4=64 kg and a velocity (magnitude) of v4=5 m/s, thus their kinetic energy is:

$\displaystyle K_4=\frac{1}{2}64\cdot 5^2$

$K_4=800\ J$

Sorted from lower kinetic energy to higher:

Lexy, Mohammed, Autumn, Chiang. Thus:

Autumn has more kinetic energy than Chiang. False

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Correct option: Mohammed has less kinetic energy than Autumn.

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2 years ago

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A single-threaded power screw is 25 mm in diameter with a pitch of 5 mm. A vertical load on the screw reaches a maximum of 5 kN.

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Answer:

0.243

Explanation:

<u>Step 1: </u> Identify the given parameters

Force (f) = 5kN, length of pitch (L) = 5mm, diameter (d) = 25mm,

collar coefficient of friction = 0.06 and thread coefficient of friction = 0.09

Frictional diameter =45mm

<u>Step 2:</u> calculate the torque required to raise the load

$T_{R} = \frac{5(25)}{2} [\frac{5+\pi(0.09)(25)}{\pi(25)-0.09(5)}]+\frac{5(0.06)(45)}{2}$

$T_{R}$ = (9.66 + 6.75)N.m

$T_{R}$ = 16.41 N.m

<u>Step 3:</u> calculate the torque required to lower the load

$T_{L} = \frac{5(25)}{2} [\frac{\pi(0.09)(25) -5}{\pi(25)+0.09(5)}]+\frac{5(0.06)(45)}{2}$

$T_{L}$ = (1.64 + 6.75)N.m

$T_{L}$ = 8.39 N.m

Since the torque required to lower the thread is positive, the thread is self-locking.

The overall efficiency = $\frac{F(L)}{2\pi(T_{R})}$

= $\frac{5(5)}{2\pi(16.41})}$

= 0.243

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2 years ago

A stretched spring has 5184 J of elastic potential energy and a spring constant of 16,200 N/m. What is the displacement of the s

Bezzdna [24]

Hello!

A stretched spring has 5184 J of elastic potential energy and a spring constant of 16,200 N/m. What is the displacement of the spring?

0.57 m

0.64 m

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Data:

$E_{pe}\:(elastic\:potential\:energy) = 5184\:J$

$K\:(constant) = 16200\:N/m$

$x\:(displacement) =\:?$

For a spring (or an elastic), the elastic potential energy is calculated by the following expression:

$E_{pe} = \dfrac{k*x^2}{2}$

Where k represents the elastic constant of the spring (or elastic) and x the deformation or displacement suffered by the spring.

Solving:

$E_{pe} = \dfrac{k*x^2}{2}$

$5184 = \dfrac{16200*x^2}{2}$

$5184*2 = 16200*x^2$

$10368 = 16200\:x^2$

$16200\:x^2 = 10368$

$x^{2} = \dfrac{10368}{16200}$

$x^{2} = 0.64$

$x = \sqrt{0.64}$

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Answer:

The displacement of the spring = 0.8 m (or 0.80 m)

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I Hope this helps, greetings ... Dexteright02! =)

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2 years ago

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