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3 years ago

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Physics

1 answer:

Over [174]3 years ago

5 0

Answer:

$\boxed {\boxed {\sf 5.22 \ m}}$

Explanation:

Gravitational potential energy is the energy an object possesses due to its position. It is calculated using the following formula:

$E_P=mgh$

Where <em>m</em> is the mass, <em>g</em> is the acceleration due to gravity, and <em>h</em> is the height.

The object has a mass of 8.72 kilograms. Assuming this occurs on Earth, the acceleration due to gravity is 9.8 meters per second squared. The object gains 446 Joules of potential energy.

Let's convert the units of Joules. This makes the process of canceling units simpler later on. 1 Joule is equal to 1 kilogram meter squared per second squared. The object gains 446 J, which is equal to 446 kg *m²/s².

EP= 446 kg*m²/s²
m= 8.72 kg
g= 9.8 m/s²

Substitute the values into the formula.

$446 \ kg*m^2/s^2 = 8.72 \ kg * 9.8 \ m/s^2 *h$

Multiply on the right side of the equation.

$446 \ kg*m^2/s^2 = 85.456 kg*m/s^2 *h$

We are solving for the height, so we must isolate the variable h. It is being multiplied by 85.456 kg*m/s². The inverse operation of multiplication is division, so we divide both sides by this value.

$\frac{ 446 \ kg*m^2/s^2}{85.456 kg*m/s^2} = \frac{85.456 kg*m/s^2 *h}{85.456 kg*m/s^2}$

$\frac{ 446 \ kg*m^2/s^2}{85.456 kg*m/s^2} =h$

The units of kg*m/s² cancel, leaving meters as our unit.

$\frac{ 446 }{85.456 } \ m =h$

$5.2190601011 \ m =h$

The original measurements of mass and potential energy have 3 significant figures, so our answer must have the same.

For the number we calculated, that is the hundredths place. The 9 in the thousandths place to the right tells us to round the 1 up to a 2.

$5.22 \ m \approx h$

The object was lifted to a height of approximately <u>5.22 meters.</u>

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2 years ago

A square is 1.0 m on a side. Point charges of +4.0 μC are placed in two diagonally opposite corners. In the other two corners ar

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Answer:

Explanation:

<u>Electric Potential Due To Point Charges </u>

The electric potential produced from a point charge Q at a distance r from the charge is

$\displaystyle V=k\frac{Q}{r}$

The total electric potential for a system of point charges is equal to the sum of their individual potentials. This is a scalar sum, so direction is not relevant.

We must compute the total electric potential in the center of the square. We need to know the distance from all the corners to the center. The diagonal of the square is

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where a is the length of the side.

The distance from any corner to the center is half the diagonal, thus

$\displaystyle r=\frac{d}{2}=\frac{a}{\sqrt{2}}$

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The total potential is

$V_t=V_1+V_2+V_3+V_4$

Where V1 and V2 are produced by the +4\mu C charges and V3 and V4 are produced by the two opposite charges of $\pm 3\mu\ C$ . Since all the distances are equal, and the charges producing V3 and V4 are opposite, V3 and V4 cancel each other. We only need to compute V1 or V2, since they are equal, but they won't cancel.

$\displaystyle V_1=V_2=k\frac{Q}{r}=9\times 10^9 \frac{4\times 10^{-6}}{0.707}$

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$V_t=50912\ V+50912\ V=1\times 10^5\ V$

$\boxed{V_t=1\times 10^5\ V}$

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Answer:

Explanation:

Expression for time period of a pendulum is as follows

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