Question

You have negotiated with the Omicronians for a base on the planet Omicron Persei 7. The architects working with you to plan the base need to know the acceleration of a freely falling object at the surface of the planet in order to adequately design the structures. The Omicronians have told you that the value is gOP7=7.29 flurggrom2, but your architects use the units metersecond2, and from your previous experience you know that both the Omicronians and your architects are terrible at unit conversion. Thus, it's up to you to do the unit conversion. Fortunately, you know the unit equality relationships: 5.24flurg=1meter and 1grom=0.493second. What is the value of gOP7 in the units your architects will use, in metersecond2?

Answer 1

5.72 m/s^2

First, we have available 2 conversion units.

5.24 flurg/m and 0.493 s/grom

I chose the units to describe those two conversions by making the denominator equal to 1 in both cases, so there are 5.24 flurgs per meter and 0.493 seconds per grom.

Now we've been given 7.29 flurg/grom^2 and we want to convert to m/s^2. So we need to figure out how to multiply or divide our conversion factors to cancel out the flurg and grom units. Let's see about cancelling the flurg unit 1st and replacing it with meters

Let's try multiplication

flurg/grom^2 * flurg/m = flurg^2/(m*grom^2)

That won't work. So let's try division

flurg/grom^2 / flurg/m

= flurg/grom^2 * m/flurg

= (m*flurg)/(grom^2 * flurg)

The flurg on top and bottom, cancel, so

= m/grom^2

So dividing by our length conversion will work correctly. Let's do it.

7.29 flurg/grom^2 / 5.24 flurg/m = 1.391221374 m/grom^2

Now we want to convert from m/grom^2 to m/(s grom) using our time conversion factor. Since we want s in the denominator and it's in the numerator, a division looks good. So

m/grom^2 / s/grom

= m/grom^2 * grom/s

= (m*grom)/(grom^2 * s)

= m/(grom * s)

And it is good. So let's do it

1.391221374 m/grom^2 / 0.493 s/grom = 2.821950049 m/(grom s)

We still have one more grom to get rid of. And since it's in the same place as the previous one, let's divide again.

2.821950049 m/(grom s) / 0.493 s/grom = 5.72403661 m/s^2

Since all our input is to only 3 significant figures, round the result to 3 significant figures. Giving 5.72 m/s^2

Answer 2

Unit conversion enables information of a given quantity to be expressed in different units by multiplying the units with the conversion factors

The value of the acceleration due to gravity on the planet Omicron Persei 7,  $g_{OP7}$ is approximately 5.724 meter/second²

Reason:

The known parameters:

The acceleration of a freely falling object on the surface of Omicron Persei 7 =   $g_{OP7} = \mathbf{7.29} \ \dfrac{flurg}{grom^2}$

The units used by the architects = $\mathbf{\dfrac{meter}{second^2}}$

5.24 flurg = 1 meter

1 grom = 0.493 second

Therefore;

$Gravity \ acceleration, \ g_{OP7} =7.29 \ \mathbf{ \dfrac{flurg}{grom^2} \times \left(\dfrac{1 \, meter}{5.24 \, flurg} \right) \times \dfrac{1 \ grom^2}{(0.493 \ second)^2}}$

$\ \dfrac{flurg}{grom^2} \times \left(\dfrac{1 \, meter}{5.24 \, flurg} \right) \times \dfrac{1 \ grom^2}{(0.493 \ second)^2} = \mathbf{0.7852 \ \dfrac{meter}{second^2}}$

Which gives;

$Gravity \ acceleration, \ g_{OP7} \approx 7.29 \times 0.7852 \ \dfrac{meter} {second^2} \approx \mathbf{5.724 \ \dfrac{meter} {second^2}}$

The value of $g_{OP7}$ in SI Units of $\mathbf{\dfrac{meter}{second^2}}$ is therefore;

$g_{OP7} \approx \mathbf{5.724 \dfrac{meter} {second^2}}$

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