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tekilochka [14]
3 years ago
11

A loaded flatbottom barge floats in fresh wa-ter. The bottom of the barge is 4.09 m belowthe water line. When the barge is empty

thebarge’s bottom is only 1.8 m below the waterline.What is the difference between the pressureon the bottom of the loaded barge and thepressure at the water line?Answer in units of Pa.006 (part 2 of 2) 10.0 pointsIf the surface area of the bottom of the barge
Physics
1 answer:
tensa zangetsu [6.8K]3 years ago
5 0

Answer:

The value is \Delta  P  =  40082 \  Pa

Explanation:

From the question we are told that

   The length of the bottom of the barge  below the water line when loaded  is d_2 =  4.09 \ m

      The length of the bottom of the barge  below the water line when empty   is d_1  =  1.80  \ m

Generally the difference in pressure is mathematically represented as

           \Delta  P  =  \rho *  g  * d_2

Here \rho is the density of water with value \rho =  1000 \  kg/m^3

           \Delta  P  =  1000 *  9.8   *  ( 4.09 )

=>        \Delta  P  =  40082 \  Pa

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A) The resultant force is 30.4 N at 25.3^{\circ}

B) The resultant force is 18.7 N at 43.9^{\circ}

Explanation:

A)

In order to find the resultant of the two forces, we must resolve each force along the x- and y- direction, and then add the components along each direction to find the components of the resultant.

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F_2 = 15 N at 60^{\circ} above y-axis

Resolving each force:

F_{1x}=F_1 cos \theta = (20)(cos 0)=20 N\\F_{1y}=F_1 sin \theta =(20)(sin 0)=0 N

F_{2x}=F_2 cos \theta = (15)(cos 60)=7.5 N\\F_{2y}=F_2 sin \theta =(15)(sin 60)=13.0 N

So, the components of the resultant are:

F_x = F_{1x}+F_{2x}=20+7.5 = 27.5 N\\F_y = F_{1y}+F_{2y}=0+13.0=13.0 N

And the magnitude of the resultant is:

F=\sqrt{F_x^2+F_y^2}=\sqrt{27.5^2+13.0^2}=30.4 N

And the direction is:

\theta=tan^{-1}(\frac{F_y}{F_x})=tan^{-1}(\frac{13.0}{27.5})=25.3^{\circ}

B)

In this case, the 15 N is applied in the opposite direction to the 20 N force. Therefore we need to re-calculate its components, keeping in mind that the angle of the 15 N force this time is

\theta=180^{\circ}-60^{\circ}=120^{\circ}

So we have:

F_{2x}=F_2 cos \theta = (15)(cos 120)=-7.5 N\\F_{2y}=F_2 sin \theta =(15)(sin 120)=13.0 N

So, the components of the resultant this time are:

F_x = F_{1x}+F_{2x}=20-7.5 = 12.5 N\\F_y = F_{1y}+F_{2y}=0+13.0=13.0 N

And the magnitude is:

F=\sqrt{F_x^2+F_y^2}=\sqrt{13.5^2+13.0^2}=18.7 N

And the direction is:

\theta=tan^{-1}(\frac{F_y}{F_x})=tan^{-1}(\frac{13.0}{13.5})=43.9^{\circ}

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