How would the number 13,900 be written using scientific notation?
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Answer:
Rotational kinetic energy = 0.099 J
Translational kinetic energy = 200 J
The moment of inertia of a solid sphere is .
Explanation:
Rotational kinetic energy is given by
where <em>I</em> is the moment of inertia and <em>ω</em> is the angular speed.
For a solid sphere,
where <em>m</em> is its mass and <em>r</em> is its radius.
From the question,
<em>ω</em> = 49 rad/s
<em>m</em> = 0.15 kg
<em>r</em> = 3.7 cm = 0.037 m
Translational kinetic energy is given by
where <em>v</em> is the linear speed.
We will use two definitions to solve this problem. The first will be given by the conservation of energy, whereby the change in kinetic energy must be equivalent to work. At the same time, work can be defined as the product between the force by the distance traveled. By matching these two expressions and clearing for the Force we can find the desired variable.
Thus the force acting on the sled is,
Replacing,
Therefore the Force acting on the sled is 32N