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1 answer:
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at the lowest point in the trajector, the kinetic energy of the bob is 300 J.
Explanation:
The total mechanical energy of the bob at any point of its motion is given by
Where
is the kinetic energy, where
m is the mass of the bob
v is its speed
is the gravitational potential energy, where
g is the acceleration of gravity
h is the height of the bob, measured with respect to the lowest point of the trajector
In absence of friction, the total mechanical energy E remains constant. So we have:
- When the bob swings upward, the PE increases (because h increases) and the KE decreases (so the speed decreases). At the highest point in the trajector, the speed of the bob is zero (v=0), so its KE is also zero and all the mechanical energy is potential energy: U = 300 J
- When the bob swings downward, the PE decreases (because h decreases) and the KE increases (so the speed increases). At the lowest point in the trajectory, the height has become zero (h=0), so the PE is zero and all the mechanical energy is kinetic energy: KE = 300 J
Therefore, at the lowest point in the trajector, the kinetic energy of the bob is 300 J.
Learn more about kinetic energy:
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Answer:
a
The New angular speed is
b
The Kinetic energy before the masses are pulled in is
c
The Kinetic energy after the masses are pulled in is
Explanation:
From the we are told that masses are 1.08 m from the axis of rotation, this means that
The radius
The mass is
The angular speed
The moment of inertia of the system excluding the two mass
New radius
Generally the conservation of angular momentum can be mathematical represented as
Where is the final angular speed
is the initial angular speed
is the initial moment of inertia
is the final moment of inertia
Moment of inertia is mathematically represented as
Where I is the moment of inertia
m is the mass
r is the radius
So the Initial moment of inertia is given as
The multiplication by is because we are considering two masses
So the final moment of inertia is given as
Substituting these values into equation 1
Generally Kinetic energy is mathematically represented in term of moment of inertia as
Now considering the kinetic energy before the masses are pulled in,
The Moment of inertia would be
The Angular speed would be
Now substituting these value into the equation above
Now considering the kinetic energy after the masses are pulled in,
The Moment of inertia would be
The Angular speed would be
Now substituting these value into the equation above