Question

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

Answer 1

4.25m

Step-by-step 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 [(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`).

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.

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

`(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):

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

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

Answer 2

h = 4.25 m

Step-by-step explanation:

`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