Nuclear decay occurs according to first-order kinetics. Cobalt-60 decays with a rate constant of 0.131 years−1. After 5.00 years
1 answer:
Answer : The original mass of the sample was 0.581 grams.
Explanation :
Expression for rate law for first order kinetics is given by:
where,
k = rate constant =
t = time passed by the sample = 5.00 years
a = original or initial amount of the reactant = ?
a - x = amount left after decay process = 0.302 g
Now put all the given values in above equation, we get
Therefore, the original mass of the sample was 0.581 grams.
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Answer:
The box stops in 0.139 seconds, after moving 7.29cm (0.0729m) backwards relative to the belt.
Explanation:
As the box is initially at rest relative to the earth, it is moving backwards with a speed of 1.05m/s relative to the belt. Then, the frictional force acts on the box to make it stop relative to the belt. So, we first have to write the equations of motion of the box in each axis:
Since the frictional force is equal to
, then we have that the acceleration is:
Now, from the definition of acceleration we get:
And, as the final velocity is zero because the box gets to a stop, we have:
(Don't worry about the negative sign. It will disappear because the initial velocity is also negative, since we take the box initially moving backwards)
Then, plugging in the given values, we calculate the time:
In words, the time the box takes to stop sliding relative to the belt is 0.139s.
The displacement of the box in this time, is given by the kinematics formula:
Finally, we calculate the displacement:
This means that the box moves 7.29cm backwards relative to the belt.