A train has an acceleration of magnitude 0.90 m/s2 while stopping. A pendulum with a 0.55-kg bob is attached to a ceiling of one
1 answer:
The angle of the pendulum with the vertical is
Explanation:
As the train decelerates, the bob of the pendulum will feel a force given by
where
m = 0.55 kg is the mass of the bob
is the magnitude of the acceleration
In the horizontal direction.
The pendulum will be inclined at an angle from the vertical, so it will be in equilibrium, and therefore the horizontal component of the tension in the string must be equal to the net force F of the previous equation:
(1)
where T is the tension in the string.
We also know that the bob is in equilibrium along the vertical direction: so the vertical component of the tension must be equal to the weight of the bob,
(2)
where is the acceleration of gravity.
Dividing eq.(1) by eq(2), we get:
And therefore, we find the angle:
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The magnetic force experienced by the proton is given by
where q is the proton charge, v its velocity, B the magnitude of the magnetic field and
the angle between the direction of v and B. Since the proton moves perpendicularly to the magnetic field, this angle is 90 degrees, so 
and we can ignore it in the formula.
For Netwon's second law, the force is also equal to the proton mass times its acceleration:
So we have
from which we can find the magnitude of the field:
where q is the proton charge, v its velocity, B the magnitude of the magnetic field and
For Netwon's second law, the force is also equal to the proton mass times its acceleration:
So we have
from which we can find the magnitude of the field:
Answer: 0.077 M
Explanation:
Expression for rate law for first order kinetics is given by:
where,
k = rate constant =
t = time taken for decay process = 10 minutes
a = initial amount of the reactant= 0.859 M
a - x = amount left after decay process =?
Putting values in above equation, we get:
Thus the concentration of a after 10.0 minutes is 0.077 M.