A small squishy ball is thrown against the side of a large cube of concrete. While the objects are in contact with each other, w
1 answer:
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Answer:
<em>0.97c</em>
<em></em>
Explanation:
From the relativistic equation for length contraction, we have
=
where
is the final length of the object
is the original length of the object before contraction
β =
where v is the speed of the object
c is the speed of light in free space = 3 x 10^8 m/s
The equation can be re-written as
/
=
For the length to contract to one-fourth of the proper length, then
/
= 1/4
substituting into the equation, we'll have
1/4 =
substituting for β, we'll have
1/4 =
squaring both side of the equation, we'll have
1/16 = 1 -
= 1 - 1/16
= 15/16
square root both sides of the equation, we have
v/c = 0.968
v = <em>0.97c</em>
<u>Answer:</u> The energy gained by the air molecules is 0.011 J.
<u>Explanation:</u>
Law of conservation of energy states that energy can neither be created nor be destroyed but it can only be transformed from one form to another form.
Here, the potential energy of the coffee filter is getting converted into kinetic energy of the coffee filter and some energy is lost by it which is gained by the air molecules in the form of kinetic energy.
So, calculating the potential energy of coffee filter, we use the equation:
P = mgh
where,
m = mass of coffee filter = 1.2 g = (Conversion used: 1 kg = 1000 g)
g = acceleration due to gravity =
h = height of coffee filter = 1 m
Putting values in above equation, we get:
- Calculating the kinetic energy of coffee filter, we use the equation:
where,
m = mass of coffee filter = 1.2 g =
v = speed of coffee filter = 0.8 m/s
Putting values in above equation, we get:
As, energy lost by coffee filter = energy gained by air molecules
So, energy lost by coffee filter = Potential energy - Kinetic energy
Energy lost by coffee filter =
Hence, the energy gained by the air molecules is 0.011 J.
Part 1) Which metal will cool the fastest?
To answer this question, we should have a look at the formula of the heat flow rate, which says "how fast" a material is able to heat/cool:
where:
is the heat exchanged
is the time interval
k is thermal conductivity of the material
A the surface where the exchange of heat occurs
the variation of temperature
x is the thickness of the material
We see that the heat flow rate
is linearly proportional to k, the thermal conductivity of the material. So, the larger k, the fastest the metal will cool.
If we have a look at the thermal conductivity of each metal, we find:
- Aluminium: 237 W/(mK)
- Copper: 401 W/(mK)
- Gold: 314 W/(mK)
- Platinum: 69 W/(mK)
Therefore, copper is the material with highest heat flow rate, so the metal which cools fastest.
Part 2) Which sample of copper demonstrates the greatest increase in temperature
To solve this part, we can have a look at how the amount of heat exchanged Q is related to the increase in temperature:
where m is the mass and Cs the specific heat of the material. Re-arranging the formula, we get
therefore, we see that the increase in temperature is inversely proportional to the mass m. This means that the block that will show the largest increase in temperature is the block with the smallest mass, so the correct answer is A) 0.5 kg.
To answer this question, we should have a look at the formula of the heat flow rate, which says "how fast" a material is able to heat/cool:
where:
k is thermal conductivity of the material
A the surface where the exchange of heat occurs
x is the thickness of the material
We see that the heat flow rate
If we have a look at the thermal conductivity of each metal, we find:
- Aluminium: 237 W/(mK)
- Copper: 401 W/(mK)
- Gold: 314 W/(mK)
- Platinum: 69 W/(mK)
Therefore, copper is the material with highest heat flow rate, so the metal which cools fastest.
Part 2) Which sample of copper demonstrates the greatest increase in temperature
To solve this part, we can have a look at how the amount of heat exchanged Q is related to the increase in temperature
where m is the mass and Cs the specific heat of the material. Re-arranging the formula, we get
therefore, we see that the increase in temperature is inversely proportional to the mass m. This means that the block that will show the largest increase in temperature is the block with the smallest mass, so the correct answer is A) 0.5 kg.