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A 2 kg stone is tied to a 0.5 m string and swung around a circle at a constant angular velocity of 12 rad/s. the angular momentu
1 answer:
Starting from the angular velocity, we can calculate the tangential velocity of the stone:
Then we can calculate the angular momentum of the stone about the center of the circle, given by
where
m is the stone mass
v its tangential velocity
r is the radius of the circle, that corresponds to the length of the string.
Substituting the data of the problem, we find
Then we can calculate the angular momentum of the stone about the center of the circle, given by
where
m is the stone mass
v its tangential velocity
r is the radius of the circle, that corresponds to the length of the string.
Substituting the data of the problem, we find
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1) 0.77 m
2) 0.23 m
Explanation:
1)
Here we want to find the time elapsed for crouching in order to jump and reach a height of 2.0 m above the floor, starting from 1.0 m above the floor.
First of all, we start by calculating the speed required to jump up to a height of 2.0 m. Since the total energy is conserved, the initial kinetic energy is converted into gravitational potential energy, so:
where
m is the mass of the man
v is the speed after jumping
is the acceleration due to gravity
h = 2.0 - 1.0 = 1.0 m is the change in height
Solving for v,
In the acceleration phase, we know that the initial velocity is
And the force exerted on the floor is 2.3 times the gravitational force, so
This means the net force on you is
because we have to consider the force of gravity acting downward.
So the acceleration of the man is
Now we can use the following suvat equation to find the displacement in the acceleration phase, which is how low the man has to crouch in order to jump:
where s is the quantity we want to find. Solving for s,
2)
At the beginning, we are told that the height of the center of mass above the floor is
h = 1.0 m
During the acceleration phase and the crouch, the height of the center of mass of the body decreases by
This means that the lowest point reached by the center of mass above the floor during the crouch is
This value seems unpractical, since it is not really easy to crouch until having the center of mass 0.23 m above the ground.
Explanation:
We will calculate the gravitational potential energy as follows.
=
= 1164000 J
or, = 1164 kJ (as 1 kJ = 1000 J)
Now, we will calculate the change in potential energy as follows.
=
=
= -873000 J
or, = -873 kJ
Thus, we can conclude that change in gravitational potential energy is -873 kJ.