Answers:
a)
b)
c)
Explanation:
We have the following data:
is the spring constant
is the amplitude of oscillation
is the velocity of the block when
Now let's begin with the answers:
<h3>a) Mass of the block</h3>
We can solve this by the conservation of energy principle:
(1)
Where:
is the initial potential energy
is the initial kinetic energy
is the final potential energy
is the final kinetic energy
Then:
(2)
Isolating :
(3)
(4)
(5)
<h3>b) Period</h3>
The period is given by:
(6)
Substituting (5) in (6):
(7)
(8)
<h3>c) Maximum acceleration</h3>
The maximum acceleration is when the force is maximum , as well :
(9)
Being
Hence:
(10)
Finding :
(11)
(12)
Finally:
Answer:at 21.6 min they were separated by 12 km
Explanation:
We can consider the next diagram
B2------15km/h------->Dock
|
|
B1 at 20km/h
|
|
V
So by the time B1 leaves, being B2 traveling at constant 15km/h and getting to the dock one hour later means it was at 15km from the dock, the other boat, B1 is at a distance at a given time, considering constant speed of 20km/h*t going south, where t is in hours, meanwhile from the dock the B2 is at a distance of (15km-15km/h*t), t=0, when it is 8pm.
Then we have a right triangle and the distance from boat B1 to boat B2, can be measured as the square root of (15-15*t)^2 +(20*t)^2. We are looking for a minimum, then we have to find the derivative with respect to t. This is 5*(25*t-9)/(sqrt(25*t^2-18*t+9)), this derivative is zero at t=9/25=0,36 h = 21.6 min, now to be sure it is a minimum we apply the second derivative criteria that states that if the second derivative at the given critical point is positive it means here we have a minimum, and by calculating the second derivative we find it is 720/(25 t^2 - 18 t + 9)^(3/2) that is positive at t=9/25, then we have our answer. And besides replacing the value of t we get the distance is 12 km.
Answer:
Evaporation is the physical change in which a substance converts from its <u>liquid</u> state to its <u>gaseous</u> state. Condensation is the physical change in which a substance converts from its <u>gaseous</u> state to its <u>liquid</u> state.
Explanation:
Evaporation and condensation are opposite processes to each other. Evaporation changes a liquid to a gas and condensation is the reverse.