Question

An automobile to be transported by ship is raised 7.0 m above the dock. If its gravitational potential energy is 66,000 J, what is the automobile’s mass

Answer 1

Answer:

$m = 1,347\ kg$

Explanation:

Gravitational Potential Energy

It's the energy stored in an object because of its vertical position or height in a gravitational field.

It can be calculated with the equation:

U=m.g.h

Where:

m = mass of the object

h  = height with respect to a fixed reference

g  = acceleration of gravity, usually taken as $9.8 m/s^2$.

The automobile of unknown mass is raised to a height of h=7 m above the dock, assumed as a reference. The automobile has gravitational potential energy of U=66,000 J.

Let's calculate the mass by solving for m:

$\displaystyle m=\frac{U}{hg}$

$\displaystyle m=\frac{66,000}{5*9.8}$

$\displaystyle m=\frac{66,000}{49}$

$\mathbf{m = 1,347\ kg}$

Answer 2

The mass of the automobile to be transported by ship is 962.1kg.

Given the data in the question;

• Height; $h = 7.0m$

• Gravitational potential energy; $U = 66,000J$

Mass of automobile; $m =\ ?$

The gravitational potential energy any object at a given height on Earth is expressed as:

$U = mgh$

Where m is mass of the object, h is height and g is acceleration due to gravity ( $g = 9.8m/s^2$ )

We substitute our given values into the equation

$66000J = m\ *\ 9.8m/s^2\ *\ 7m\\\\66000kg.m^2/s^2 = m\ *\ 9.8m/s^2\ *\ 7m\\\\66000kg.m^2/s^2 = m\ *\ 68.6m^2/s^2\\\\m = \frac{66000kg.m^2/s^2}{68.6m^2/s^2} \\\\m = 962.1 kg$

Therefore, the mass of the automobile to be transported by ship is 962.1kg.

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