Answer:
0.102 m
Explanation:
k = spring constant of the spring = 125 N/m
m = mass of the block attached to the spring = 650 g = 0.650 kg
x = maximum extension of the spring
h = height dropped by the block = x
Using conservation of energy
Spring potential energy gained = Gravitational potential energy lost
(0.5) k x² = mgh
(0.5) k x² = mgx
(0.5) (125) x = (0.650) (9.8)
x = 0.102 m
Compressional waves can travel through all states of matter.
Answer:
The temperature of the core raises by every second.
Explanation:
Since the average specific heat of the reactor core is 0.3349 kJ/kgC
It means that we require 0.3349 kJ of heat to raise the temperature of 1 kg of core material by 1 degree Celsius
Thus reactor core whose mass is will require
energy to raise it's temperature by 1 degree Celsius in 1 second
Hence by the concept of proportionately we can infer 150 MW of power will increase the temperature by
Answer:
h'=0.25m/s
Explanation:
In order to solve this problem, we need to start by drawing a diagram of the given situation. (See attached image).
So, the problem talks about an inverted circular cone with a given height and radius. The problem also tells us that water is being pumped into the tank at a rate of . As you may see, the problem is talking about a rate of volume over time. So we need to relate the volume, with the height of the cone with its radius. This relation is found on the volume of a cone formula:
notie the volume formula has two unknowns or variables, so we need to relate the radius with the height with an equation we can use to rewrite our volume formula in terms of either the radius or the height. Since in this case the problem wants us to find the rate of change over time of the height of the gasoline tank, we will need to rewrite our formula in terms of the height h.
If we take a look at a cross section of the cone, we can see that we can use similar triangles to find the equation we are looking for. When using similar triangles we get:
When solving for r, we get:
so we can substitute this into our volume of a cone formula:
which simplifies to:
So now we can proceed and find the partial derivative over time of each of the sides of the equation, so we get:
Which simplifies to:
So now I can solve the equation for dh/dt (the rate of height over time, the velocity at which height is increasing)
So we get:
Now we can substitute the provided values into our equation. So we get:
so: