Answer:
1/2
Explanation:
We need to make a couple of considerations but basically the problem is solved through the conservation of energy.
I attached a diagram for the two surfaces and begin to make the necessary considerations.
Rough Surface,
We know that force is equal to,



Matching the two equation we have,


Applying energy conservation,





Frictionless surface




Given the description we apply energy conservation taking into account the inertia of a sphere. Then the relation between
and
is given by


Answer:
c. 972
Explanation:
The volume of a rectangular solid is calculated as the product of its dimensions, that is, its width, its length and its height:

1 feet is equal to 12 inches, so:

Now, we calculate the volume of the object in cubic inches:

Answer:
t=37 mins -> 2220sec
We want "T" which is the pendulum time constant
Using this equation
.5A=Ae^(-t/T)
The .5A is half the amplitude
Take ln of both sides to get ride of Ae
=ln(.5)=-2220/T
Now rearrange to = T
T=-2220/ln(.5) = 3202.78sec / 60 secs = 53.38 mins -> first part of the answer.
The second part is really easy. It took 37 mins to decay half way. meaning to decay another half of 50% which equals 25% it will take an additional 37 mins!
To solve this problem it is necessary to apply the concepts related to thermal stress. Said stress is defined as the amount of deformation caused by the change in temperature, based on the parameters of the coefficient of thermal expansion of the material, Young's module and the Area or area of the area.

Where
A = Cross-sectional Area
Y = Young's modulus
= Coefficient of linear expansion for steel
= Temperature Raise
Our values are given as,




Replacing we have,


Therefore the size of the force developing inside the steel rod when its temperature is raised by 37K is 38526.1N