A thin rod of length 0.83 m and mass 110 g is suspended freely from one end. It is pulled to one side and then allowed to swing
2 answers:
Explanation:
(a) The given data is as follows.
Length of the rod, L = 0.83 m
Mass of the rod, m = 110 g = 0.11 (as 1 kg = 1000 g)
At the lowest point, angular speed of the rod () = 5.71 rad/s
First, we will calculate the rotational inertia of the rod about an axis passing through its fixed end is as follows.
I =
=
=
= 0.00631 + 0.415
= 0.42131
Therefore, kinetic energy of the rod at its lowest point will be calculated as follows.
K =
=
= 6.86 J
Hence, kinetic energy of the rod at its lowest point is 6.86 J.
(b) According to the conservation of total mechanical energy of the rod, we have
or, mgh = K = 6.86 J
Therefore, h =
=
= 0.584 m
Hence, the center of mass rises 0.584 m far above that position.
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Answer:
At the point of dropping the object, by Newton's first law due to gravitational force = m × g, accelerates
By Newton's Second law the object reaches impacts on the air with the gravitational force resulting in changing momentum of m×(Final Velocity - Initial Velocity)
As the velocity increases, the rate of change of momentum becomes equivalent to the gravitational force and by Newton's third law, the action action and reaction are equal and opposite hence they cancel each other out
The body then moves at a constant uniform motion down according to Newton's first law
Explanation:
At the point the object of mass, m, is dropped from the height of the tower, the only force acting on the object is the gravitational force such that the object has an acceleration which is the acceleration due to gravity, g, and the gravitational force is therefore = m × g
As the speed of the object increases while the object is falling with the gravitational acceleration the rate at which the object cuts through layers of air which (by Newton's first law of motion, are at rest ) has some buoyancy effect also increases therefore, the object is constantly increasingly changing the momentum of the air which by Newton's second law results, at an high enough velocity, and by Newton's third law, in a force equal to the applied gravitational force
Therefore, the force of the air drag becomes equal to the gravitational force, cancelling each other out and the object then moves according to Newton;s first law, in uniform motion of a constant speed while still falling down.