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Andrews [41]
3 years ago
14

The period of a simple pendulum, defined as the time necessary for one complete oscillation, is measured in time units and is gi

ven by
T = 2π×square root of l/g

where ℓ is the length of the pendulum and g is the acceleration due to gravity, in units of length divided by time squared. Show that this equation is dimensionally consistent.
Physics
1 answer:
Oksana_A [137]3 years ago
7 0

The task is to show that the right side of the equation has units of [Time], just like the left side has.

The right side of the equation is . . . 2 π √(L/G) .

We can completely ignore the  2π since it has no units at all, so it has no effect on the units of the right side of the equation.  Now the task is simply to find the units of  √(L/G) .

L . . . meters

G . . . meters/sec²

(L/G) = (meters) / (meters/sec²)

(L/G) = (meters) · (sec²/meters)

(L/G) = (meters · sec²) / (meters)

(L/G) = sec²

So  √(L/G) = seconds = [Time]

THAT's what we were hoping to prove, and we did it !

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2.72 Kilometers

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3 years ago
7. If 8 million kg of water flows over Niagara Falls each second, calculate the power available at the bottom of the falls.
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Answer:

The power will be "3.92×10⁹ Watts". A further explanation is given below.

Explanation:

The given values as per the question,

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As we know,

The power will be:

⇒ Power = Rate\times Distance\times  Gravity

On putting the values, we get

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If gravity between the Sun and Earth suddenly vanished, Earth would continue moving in
Ksenya-84 [330]

Answer:

Earth would continue moving by uniform motion, with constant velocity, in a straight line

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This means that if there are no forces acting on an object, the object stays at rest (if it was not moving previously) or it continues moving with same velocity (if it was already moving) in a straight line.

In this problem, the Earth is initially moving around the Sun, with a certain tangential velocity v. When the Sun disappears, the force of gravity that was keeping the Earth in circular motion disappears too: therefore, there are no more forces acting on the Earth, and so by the 1st law of Newton, the Earth will continue moving with same velocity v in a straight line.

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