Answer & Explanation
Determine the system's overall potential change. m2 and m3 are the masses at the rod ends. note the rod centre of mass neither gains nor loses potential.
Determine the rod's moment of inertia.
determine the end masses' moment of inertia
compare the system's kinetic energy to the change in potential energy.
Calculate velocity at lowest point:
Length of rod
Mass of slender rod
Sphere Bob at one end
Sphere Bod at the other end
Linear speed of mass 2 at the lowest point
We need to calculate the change in potential of the complete system. m2 and m3 are the masses at the rod ends. note the rod centre of mass neither gains nor loses potential.
So, at the lowest point,
Note, at the lowest point, the mass 1 is 40cm (0.4m) form the midpoint, Also, the mass 2 is
Now, the moment of inertia of the rod is given as
calculating of inertia of the end masses.
Now, the Energy of the masses due to angular velocity is given as
Using conservation of energy
The potential energy is equal to the kinetic energy of the system
The PE of an object is the amount of energy the object will store because it is at a certain height.
The PE is given as
where m= mass of the object, g= acceleration due to gravity, and h= height.
The PE of the system is given by
Again, PE of the system is given by
The linear velocity is given by
Hence, the required velocity is 1.462m/s
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