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Nimfa-mama [501]
2 years ago
5

A book with a mass of 1.2 kg sits on a bookshelf. if it has a gravitational potential energy of 50 j, how high is the shelf? the

acceleration of gravity is 9.8m/s^2
Physics
2 answers:
sdas [7]2 years ago
7 0

Answer:

4.25m

Explanation:

Joules is a "derived unit", meaning it is really composed of other units, and it is just abbreviated as a single letter.

1[J]=1 [\frac{kg \cdot m^2}{s^2}]

This comes from the formula for potential energy, often denoted "U"

U=mgh, where m is the mass of the object (measured in kilograms,  kg), g is the acceleration due to gravity at that spot (measured in meters per second squared,  \frac {m}{s^2}), and h is the height of the object (measured in meters, m).

<em>Note:  The object itself may or may not have an acceleration of "g" at the given point because it may be supported (like on a bookshelf).  However, the "g" is representative of its gravitational acceleration at that point if gravity could accelerate it unimpeded.</em>

Rearranging the potential energy equation to isolate the unknown "h", dividing both sides by "m" and "g", we get the following:

\dfrac{U}{mg}=h

Substituting known values (and rewriting Joules as its SI units so we can ensure units cancel the way we need them to):

\dfrac{\left (50 [\frac{kg \cdot m^2}{s^2}] \right)}{(1.2 [kg])(9.8 [\frac{m}{s^2}])}=h\\\dfrac{\left (50 [\frac{kg \!\!\!\!\!\!\!{--} \cdot m^{2 \!\!\!{-}}}{s^2\!\!\!\!\!\!\!{--} }] \right)}{(1.2 [kg \!\!\!\!\!\!\!{--} ])(9.8 [\frac{m\!\!\!\!\!\!\!{--} }{s^2\!\!\!\!\!\!\!{--} }])}=h\\\dfrac{(50)}{(1.2)(9.8)}[m]=h\\\\4.2517[m] \approx h

Thus, the height of the book would be approximately 4.25meters high.

dalvyx [7]2 years ago
5 0

<u>Answer:</u>

h = 4.25 m

<u>Explanation:</u>

gravitational \space\ potential \space\ energy \space\ (gpe)= m g h\\ ,

where m is the mass, g is acceleration of gravity, and h is height of object.

In our case, m = 1.2 kg, g = 9.8m/s², and gpe = 50 J.

50 = 1.2 x 9.8 x h

h = 50 / (1.2 x 9.8)

h = 4.25 m

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