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Sergeeva-Olga [200]

3 years ago

11

A potential energy function for a system in which a two-dimensional force acts is of the form U = 3x6y − 5x. Find the force that

acts at the point (x, y). (Use the following as necessary: x and y.)

1 answer:

liq [111]3 years ago

7 0

Answer:

Force, $F=((-18x^5y+5)i+(-3x^6)j)\ N$

Explanation:

Given that,

A potential energy function for a system in which a two-dimensional force acts is of the form of :

$U=3x^6y-5x$

We need to find the force that acts at the point (x, y). The force in 2 dimensional with components is given by :

$F=(\dfrac{-dU}{dx},\dfrac{-dU}{dy})\\\\F=(\dfrac{-d(3x^6y-5x)}{dx},\dfrac{d(3x^6y-5x)}{dy})\\\\F=(-(18x^5y-5)),(-(3x^6))\\\\F=((-18x^5y+5)i+(-3x^6)j)\ N$

So, the force acting at the point (x,y) is $((-18x^5y+5)i+(-3x^6)j)\ N$ . Hence, this is the required solution.

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Suppose that a balloon is being filled with air at a rate of 10 cm3/s. (Assume that theballoon is a perfect sphere.) At what rat

Basile [38]

Answer:

Therefore the surface area of the balloon is increased at 4 cm³/s.

Explanation:

The balloon is being filled with air at a rate of 10 cm³/s

It means the volume of the balloon is increased at a rate 10 cm³/s.

i.e $\frac{dv}{dt} =10 cm^3/s$

Consider r be the radius of the balloon.

The volume of of a sphere is

$v=\frac{4}{3} \pi r^3$

Differentiate with respect to t

$\frac{dv}{dt} =\frac{4}{3} \pi \times 3r^2\frac{dr}{dt}$

$\Rightarrow 10 =4\pi r^2\frac{dr}{dt}$

$\Rightarrow \frac{dr}{dt}=\frac{10}{4\pi r^2}$

The surface of area of the balloon is(S) = $4\pi r^2$

$S=4\pi r^2$

Differentiate with respect to t

$\frac{dS}{dt} =4\pi\times2r\frac{dr}{dt}$

$\Rightarrow \frac{dS}{dt} =8\pi r\frac{dr}{dt}$

Putting the value of $\frac{dr}{dt}$

$\Rightarrow \frac{dS}{dt} =8\pi r\times\frac{10}{4\pi r^2}$

$\Rightarrow \frac{dS}{dt} =\frac{20}{ r}$

Given that r = 5 cm

$[\frac{dS}{dt}]_{r=5} =\frac{20}{ 5}$ =4 cm³/s

Therefore the surface area of the balloon is increased at 4 cm³/s.

5 0

3 years ago

If the distance between the Earth and Moon were half what it is now, by what factor would the force of gravity between them be c

hichkok12 [17]

Answer:

4

Explanation:

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

$m_1$ = Mass of Earth

$m_2$ = Mass of Moon

r = Distance between Earth and Moon

Old gravitational force

$F_o=\dfrac{Gm_1m_2}{r^2}$

New gravitational force

$F_n=\dfrac{Gm_1m_2}{(\dfrac{1}{2}r)^2}$

Dividing the equations

$\dfrac{F_n}{F_o}=\dfrac{\dfrac{Gm_1m_2}{(\dfrac{1}{2}r)^2}}{\dfrac{Gm_1m_2}{r^2}}\\\Rightarrow \dfrac{F_n}{F_o}=\dfrac{\dfrac{Gm_1m_2}{\dfrac{1}{4}r^2}}{\dfrac{Gm_1m_2}{r^2}}\\\Rightarrow \dfrac{F_n}{F_o}=4$

The ratio is $\dfrac{F_n}{F_o}=4$

The new force would be 4 times the old force

7 0

3 years ago

30 km/h is _________m/s?<br> A.)8.3<br> B.)5.6<br> C.)13.9<br> D.)11.1

Juli2301 [7.4K]

Answer:

Correct Option :- A

Explanation:

3 0

2 years ago

Which two quantities below can be used to calculate average speed?

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Change of position and time

6 0

3 years ago

Two rocks of different masses are rolling down a hill at the same speed. Which rock (small one or big one) would have more kinet

aivan3 [116]

Answer:

Kinetic energy of bigger rock will be more than that of smaller one.

Explanation:

Kinetic energy of the rock is given by,

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As velocity of both the rocks are same. Thus, kinetic energy is directly proportional to the mass of the rock

Kinetic energy ∝ mass

So, For greater mass kinetic energy will be greater and for smaller mass kinetic energy will be smaller.

Hence, Kinetic energy of bigger rock will be more than that of smaller one.

3 0

3 years ago

Read 2 more answers