Three balls are in water. Ball 1 floats, with half of it exposed above the water level. Ball 2, with a density less than the den
2 answers:
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Answer:
Part(a): The angular acceleration is .
Part(b): The angular displacement is .
Explanation:
Part(a):
If be the initial angular speed, final angular speed and angular acceleration of the centrifuge respectively, then from rotational kinematic equation, we can write
where '' is the time taken by the centrifuge to increase its angular speed.
Given, ,
and
. From equation (
), the angular acceleration is given by
Part(b):
Also the angular displacement () can be written as
Answer:
a)
b)Does not affect the long term.
Explanation:
Given that
A = A0 cos(ωt)
This is linear equation so integration factor ,I
Now by using linear equation property
b)
at t= 0
So the initial condition does not affect the long term.
a) The speed of the student after the jump is 1.07 m/s
b) The final speed of the laser is 10.4 m/s
Explanation:
a)
We can solve this problem by applying the law of conservation of momentum: if there are no external forces acting on the system, the total momentum of the student+Laser system must be constant. Therefore, we can write:
where
The initial momentum is zero
m = 42 kg is the mass of the Laser
v = 1.5 m/s is the final velocity of the Laser
M = 59 kg is the mass of the student
V is the final velocity of the student
Solving the equation for V, we find the velocity of the student:
So, the final speed of the student is 1.07 m/s.
b)
In this case, the laser and the student are travelling at 3.1 m/s before the student jumps off: therefore, the total momentum before the jump is not zero.
So, the equation of the conservation of momentum is
where
m = 42 kg is the mass of the Laser
M = 59 kg is the student's mass
u = 3.1 m/s is the initial velocity of the student and the Laser
V = -2.1 m/s is the velocity of the student after the jump (she jumps backward)
v is the final velocity of the Laser
And solving for v, we find
Learn more about momentum:
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