1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mariana [72]
3 years ago
7

A triangular plate with height 6 ft and a base of 7 ft is submerged vertically in water so that the top is 2 ft below the surfac

e. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Recall that the weight density of water is 62.5 lb/ft3.)

Physics
1 answer:
xenn [34]3 years ago
6 0

Answer:

62.5\int\limits^6_0 {(\frac{7}{6}y^{2}-\frac{49}{3}y+56)  } \, dy = 7875 lb

Explanation:

For this problem to be easier to calculate, we can represent the triangle as a right triangle whose right angle is located at the origin of a coordinate system. (See picture attached).

With this disposition of the triangle, we can start finding our integral. The hydrostatic force can be set as an integral with the following shape:

\int\limits^a_bγhxdy

we know that γ=62.5 lb/ft^{3}

from the drawing, we can determine the height (or depth under the water) of each differential area is given by:

h=8-y

x can be found by getting the equation of the line, which we'll get by finding the slope of the line and using one of the points to complete the equation:

m=\frac{y_{2}-y_{1}}{x_{2}-x{1}}

when substituting the x and y-values given on the graph, we get that the slope is:

m=\frac{0-6}{7-0}=-\frac{6}{7}

once we got this slope, we can substitute it in the point-slope form of the equation:

y_{2}-y_{1}=m(x_{2}-x_{1})

which yields:

y-6=-\frac{6}{7}(x-0)

which simplifies to:

y-6=-\frac{6}{7}x

we can now solve this equation for x, so we get that:

x=-\frac{7}{6}y+7

with this last equation, we can substitute everything into our integral, so it will now look like this:

\int\limits^6_0{(62.5)(8-y)(-\frac{7}{6}y+7)}\,dy

Now that it's all written in terms of y we can now simplify it, so we get:

62.5\int\limits^6_0 {(\frac{7}{6}y^{2}-\frac{49}{3}y+56)}dy

we can now proceed and evaluate it.

When using the power rule on each of the terms, we get the integral to be:

62.5[\frac{7}{18}y^{3}-\frac{49}{6}y^{2}+56y]^{6}_{0}

By using the fundamental theorem of calculus we get:

62.5[(\frac{7}{18}(6)^{3}-\frac{49}{6}(6)^{2}+56(6))-(\frac{7}{18}(0)^{3}-\frac{49}{6}(0)^{2}+56(0))]

When solving we get:

62.5\int\limits^6_0 {(\frac{7}{6}y^{2}-\frac{49}{3}y+56)  } \, dy = 7875 lb

You might be interested in
the nucleus and the subatomic particles in the nucleus, what is the charge of the nucleus of an atom?
pychu [463]
The Nucleus contains Protons and Neutrons.

The Neutrons does not have a charge.

The Protons are positively charge.

Hence the charge on the Nucleus, would be the charge of the proton, which is positive.

Hence Nucleus is Positively Charged.
4 0
3 years ago
Which statement best defines inertia? An object's motion is unaffected by any external forces acting upon it. An object responds
svetoff [14.1K]

Answer:

An object responds to a force by tending to move in the direction of that force

Explanation:

The inertia of a body can be defined with the help of Newton's second law

          F = m a

Where F is the applied force, a is the acceleration of the body and m is the mass

the force and the acceleration are vectors that point in the same direction and m is a scalar constant that relates the two vectors, this scalar constant is called masses and it measures the resistance of the bodies to the change of motion.

From the previous statement we see that the statement that best describes inertia is:

An object responds to force by tending to move in the direction of the force.

4 0
3 years ago
The main difference between a psychologist and a psychiatrist is that a psychiatrist can typically __________ and most psycholog
Aloiza [94]
A. prescribe medication
5 0
2 years ago
Read 2 more answers
What type of energy does the box have after it is done being pulled?
Ksivusya [100]
Assuming that the box is moving when it is being pulled, Work is done on the box.

So work is the Force times the distance

W=Fd

But what is work actually ? When something moves due to force over some change in distance, it have energy.

But where does this energy come from ? Does it magically appear ? The energy comes from the applied force onto the box.

So the energy have been transferred. And it’s like that throughout the universe

Now to save time, I’ll just tell you the answer: kinetic energy

:)
3 0
3 years ago
The temperature of a room is 77°F what would be the temperature in Celsius scale​
anygoal [31]

Formulas change from F to degree C : C = ( F - 32 )/1.8

so we have (77-32)/1.8 = 25 oC

ok done. Thank to me :>

5 0
3 years ago
Other questions:
  • A plastic rod that has been charged to -21 nc touches a metal sphere. afterward, the rod's charge is -8 nc. (a) what kind of cha
    13·1 answer
  • Water that soaks into Earth may become _____ under the surface.
    13·1 answer
  • Astronomers analyze starlight to determine a star’s (a) temperature; (b) composition; (c) motion; (d) all of the above.
    10·1 answer
  • What impulse occurs when an average force of 7.0 N is exerted on a cart for 2.5 s ?
    14·1 answer
  • Pluto has a shape that is nearly round, and it orbits the Sun. It has five known moons. Why is it called a dwarf planet and not
    6·1 answer
  • Force
    13·1 answer
  • A car takes off from a stop sign and is going 267 m/s after 4.5 seconds. a) Determine the acceleration of the car. Show your wor
    14·1 answer
  • Rest and motion are relative terms. write in brief​
    5·1 answer
  • A torsional pendulum is formed by attaching a wire to the center of a meter stick with a mass of 5.00 kg. If the resulting perio
    15·1 answer
  • what is the change in thermal energy of 1.00 kg of water that is raised from 20.0 degrees Celsius to boiling point?​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!