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3 years ago

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A single, non-constant force acts in the x direction on an object of mass m that is constrained to move along the x-axis. As a r

esult the object\'s position as a function of time is:x(t)=P+Qt+Rt^3How much work is done by this force from t = 0 s to final time T? Express your answer in terms of P, Q, R, m, and T.

1 answer:

Serhud [2]3 years ago

7 0

Answer:

Work done is given as

$W = \frac{1}{2}m(2Q + 3RT^2)(3RT^2)$

Explanation:

As we know that the position of object is given as

$x(t) = P + Qt + Rt^3$

now we know that rate of change in position of object is known as velocity

so we have

$v = \frac{dx}{dt}$

$v = Q + 3Rt^2$

now we have

initial speed at t = 0

$v_i = Q$

at t = T final speed is given as

$v_f = Q + 3RT^2$

now work done is change in kinetic energy

$W = \frac{1}{2}m(v_f^2 - v_i^2)$

$W = \frac{1}{2}m[(Q + 3RT^2)^2 - Q^2]$

$W = \frac{1}{2}m(2Q + 3RT^2)(3RT^2)$

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If you are lying down and stand up quickly, you can get dizzy or feel faint. This is because the blood vessels don't have time t

sammy [17]

Complete Question

If you are lying down and stand up quickly, you can get dizzy or feel faint. This is because the blood vessels don’t have time to expand to compensate for the blood pressure drop. If your brain is 0.4 m higher than your heart when you are standing, how much lower is your blood pressure at your brain than it is at your heart? The density of blood plasma is about 1025 kg/m3 and a typical maximum (systolic) pressure of the blood at the heart is 120 mm of Hg (= 0.16 atm = 16 kP = 1.6 × 104 N/m2).

Answer:

The pressure at the brain is $P_b = 89.872 \ mm \ of \ Hg$

Explanation:

Generally is mathematically denoted as

$P = \rho gh$

Substituting $1025 kg/m^3$ for $\rho$ (the density) , $9.8 m/s^2$ for g (acceleration due to gravity) , 0.4m for h (the height )

We have that the pressure difference between the heart and the brain is

$P = 1025 * 9.8 *0.4$

$= 4018 N/m^2$

But the pressure of blood at the heart is given as

$P_h=120 mm of Hg =$ $120 * 133 = 1.59*10^3Pa$

Now the pressure at the brain is mathematically evaluated as

$P_b = P_h - P$

$= 1.596*10^4 - 4018$

$= 11982 N/m^2$

$P_b= \frac{11982}{133} = 89.872 \ mm \ of \ Hg$

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4 years ago

This is an example of a(n)

Maurinko [17]

Answer:

Its A.

Correct me if I'm wrong.

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3 years ago

Read 2 more answers

Solve using correct significant figures and indicating maximum absolute uncertainty.

Vera_Pavlovna [14]

We use the criterion of significant figures to find the result with reliable figures

X = 9.2 10-5

now with the propagation of errors we obtain the result with its uncertainty

X ± ΔX = (9.2 ± 0.5) 10⁻⁵

given Parameter

* expression values with their absolute errors

to find

* the result with the correct significant figures

* the absolute error of the expression

Significant figures are defined with the number of decimals that give information, the number of figures in a quantity gives information about the uncertainty of this quantity.

There are two criteria for applying significant figures:

* Add and subtract the result of going with the number of decimal places of the figure that has the least

* Product and division as a result of going with the least number of significant figures than the value that has the least.

Remember that the zero to the left do not form a pair of the significant figures

Let's apply this belief to the case presented, let's write the precaution

$x = \frac{a-b}{c}$

where in this case they are worth

a = 0.0336 ± 0.0002

b = 0.010 ± 0.001

c = 255.4 ± 0.4

We see that the significant figures of each parameterize (a, b, c) and their absolute errors are correct.

Let's apply the criteria to the operation

a-b = 0.0336 - 0.010

a- b = 0.0236

we apply the criterion of significant figures for the subtraction, the result must be with 3 decimal places

a - b = 0.024

let's do the other operation

X = $\frac{a-b}{c}$

X = 0.024 / 255.4

X = 9.24 10⁻⁵

We apply the criterion of significant figures for the division, in this case the result is left with two significant figures

X = 9.2 10⁻⁵

The uncertainty or error of the measurements is of most importance as it determines how many significative figures are reliable at a given magnitude.

If the magnitudes are measured with some type of instrument, the absolute error is given by the appreciation of the instrument, if the magnitude is calculated using some equation, the errors must be propagated using the variations of each parameter in the worst case.

the uncertainty of the calculated quantity (X) is

$\Delta X = | \frac{dX}{da}| \Delta a + | \frac{dX}{db} | \Delta b + | \frac{dX}{dc}| \Delta c$

let's perform the derivatives

$\frac{dX}{da} = \frac{1}{c}$

$\frac{dX}{db} = - \frac{1}{c}$

$\frac{dX}{dc} = - \frac{a-b}{c^2}$

we substitute

remember that the bulk value guarantees that we tune the worst case. So all the mistakes add up

ΔX = $\frac{1}{c}$ Δa + $\frac{1}{c}$ Δb + $\frac{a-b}{c^2}$ Δc

ΔX = $\frac{1}{c}$ (Δa + Δb) + $\frac{a-b}{c^2}$ Δc

we substitute

ΔX = $\frac{1}{255.4}$ (0.0002 + 0.001) + $\frac{0.0336-0.010}{255.4^2}$ 0.4

ΔX = 4.698 10⁻⁶ + 1.45 10⁻⁷

DX = 4.8 10-6

Absolute errors must be given with a single significant figure

ΔX = 5 10⁻⁶

The result of the requested quantity using the criterion of significant figures and propagation of errors is

X ± ΔX = (9.2 ± 0.5) 10⁻⁵

learn more about significative figure here:

brainly.com/question/18955573

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3 years ago

A 185 g block is pressed against a spring of force constant 1.60 kN/m until the block compresses the spring 10.0 cm. The spring

denis-greek [22]

Answer:

d = 5.10 m

Explanation:

As we know that here on the plane of the inclined there is no frictional force

So in these cases we can say that total mechanical energy will always remains conserved

so here we can say that

spring potential energy = gravitational potential energy of the block

as we know from the formula

$\frac{1}{2}kx^2 = mgh$

now plug in the values in it

$\frac{1}{2}(1.60 \times 10^3)(0.10)^2 = (0.185)(9.81)h$

$8 = 1.81 h$

$h = 4.42 m$

now as we know that the angle of inclination is 60 degree and height raised is 4.42 m

so here maximum distance moved along the inclined plane will be

$\frac{h}{d} = sin60$

$d = \frac{h}{sin60}$

$d = \frac{4.42}{sin60} = 5.10 m$

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3 years ago

Consider a collection of charges in a given region and suppose all other charges are distant and have a negligible effect. Furth

AlladinOne [14]

Answer:

E. Some charges in the region are positive, and some are negative.

Explanation:

Electric potential is given as;

$V = \frac{W}{Q}$

where;

W is the work done in moving a charge between two points which have a difference in potential

Q is quantity of charge in the given region

If the electric potential at a given point in the region is zero, then sum of the charges in the given region must be equal to zero. For the charges to sum to zero, some will be positive while some will be negative,.

Therefore, the correct statement in the given options is "E"

E. Some charges in the region are positive, and some are negative.

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4 years ago