Answer:
Explanation:
Here mass density of rod is varying so we have to use the concept of integration to find mass and location of center of mass.
At any distance x from point A mass density
Lets take element mass at distance x
dm =λ dx
mass moment of inertia
So total moment of inertia
By putting the values
By integrating above we can find that
Now to find location of center mass
Now by integrating the above
So mass moment of inertia and location of center of mass
1) The mass of the continent is
2) The kinetic energy of the continent is 1683 J
3) The speed of the jogger must be 6.57 m/s
Explanation:
1)
The continent can be represented as a slab of size
and depth
So its volume is
We also know that the density of the continent is
Therefore, we can calculate its mass as:
2)
The kinetic energy of the continent is given by
where
m is its mass
v is its speed
We have already calculate its mass, while the speed is
v = 3.2 cm/year
We have to convert into SI units first, as follows:
The mass is
So, the kinetic energy of the continent is
3)
Here we have a jogger having the same kinetic energy of the continent, so
And the kinetic energy of the jogger can be expressed as
where
m = 78 kg is the mass of the jogger
v is his speed
We can therefore re-arrange the equation to find the speed of the man, and we get:
Learn more about kinetic energy:
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