If a 1,000-kg car is traveling at 20.0 m/s when it reaches the bottom of a circular hill of radius 8.00 m, what normal force doe
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Answer: A. 23.59 minutes.
B. 249.65 minutes
Explanation: This question involves the concept of Latent Heat and specific heat capacities of water in solid phase.
<em>Latent heat </em><em>of fusion </em>is the total amount of heat rejected from the unit mass of water at 0 degree Celsius to convert completely into ice of 0 degree Celsius (and the heat required for vice-versa process).
<em>Specific heat capacity</em> of a substance is the amount of heat required by the unit mass of a substance to raise its temperature by 1 kelvin.
Here, <u>given that</u>:
- mass of ice, m= 0.555 kg
- temperature of ice, T= -16.6°C
- rate of heat transfer,
- specific heat of ice,
- latent heat of fusion of ice,
<u>Asked:</u>
1. Time require for the ice to start melting.
2. Time required to raise the temperature above freezing point.
Sol.: 1.
<u>We have the formula:</u>
Using above equation we find the total heat required to bring the ice from -16.6°C to 0°C.
Now, we require 19347.3 joules of heat to bring the ice to 0°C and then on further addition of heat it starts melting.
∴The time required before the ice starts to melt is the time required to bring the ice to 0°C.
= 23.59 minutes.
Sol.: 2.
Next we need to find the time it takes before the temperature rises above freezing from the time when heating begins.
<em>Now comes the concept of Latent heat into the play, the temperature does not starts rising for the ice as soon as it reaches at 0°C it takes significant amount of time to raise the temperature because the heat energy is being used to convert the phase of the water molecules from solid to liquid.</em>
From the above solution we have concluded that 23.59 minutes is required for the given ice to come to 0°C, now we need some extra amount of energy to convert this ice to liquid water of 0°C.
<u>We have the equation:</u> latent heat,
<u>Now the time required for supply of 185370 J:</u>
t= 226.06 minutes
∴ The time it takes before the temperature rises above freezing from the time when heating begins= 226.06 + 23.59
= 249.65 minutes
1) No
2) Yes
3) No
4) Equal and opposite
5) 32400 N
6) Repulsive
7) The electric force is times bigger than the gravitational force
Explanation:
1)
In nature, the minimum possible charge that an object can have is the charge of the electron, which is called fundamental charge:
Electrons are indivisible particles (they cannot be separated), this means that an object can have at least the charge equal to the charge of one electron (in fact, it cannot have a charge less than , because it would meant that the object has a "fractional number" of electrons).
In this problem, the object has a charge of
If we compare this value to , we notice that
, so no object can have a charge of
.
2)
As we said in part 1), an object should have an integer number of electrons in order to be charged.
This means that the charge of an object must be an integer multiple of the fundamental charge, so we can write it as:
where
Q is the charge of the object
n is an integer multiple
e is the fundamental charge
Here we have
Substituting the value of e, we find n:
n is integer, so this value of the charge is possible.
3)
We now do the same procedure for the new object in this part, which has a charge of
Again, the charge on this object can be written as
where
n is the number of electrons in the object
Using the value of the fundamental charge,
We find:
n is not integer, so this value of charge is not possible, since an object cannot have a fractional number of electrons.
4)
To solve this part, we use Newton's third law of motion, which states that:
"When an object A exerts a force on an object B (Action force), then object B exerts an equal and opposite force on object A (reaction force)".
In this problem, we have two objects:
- A charge Q
- A charge 5Q
Charge Q exerts an electric force on charge 5Q, and we can call this action force. At the same time, charge 5Q exerts an electric force on charge Q (reaction force), and according to Newton's 3rd law, the two forces are equal and opposite.
5)
The magnitude of the electric force between two single-point charges is
where
k is the Coulomb's constant
q1, q2 are the two charges
r is the separation between the two charges
In this problem we have:
is charge 1
is charge 2
r = 0.30 cm = 0.003 m is the separation
So, the electric force between the two charges is
6)
The electric force between two charged objects has direction as follows:
- If the two objects have charges of opposite signs (+ and -), the force between them is attractive
- If the two objects have charges of same sign (++ or --), the force between them is repulsive
In this problem, the two charges are:
is charge 1
is charge 2
We see that the two charges have same sign: therefore, the force between them is repulsive.
7)
The electric force between the proton and the electron in the atom can be written as
where
is the magnitude of the charge of the proton and of the electron
is the separation between them
So the force can be rewritten as
The gravitational force between the proton and the electron can be written as
where
G is the gravitational constant
is the proton mass
is the electron mass
Comparing the 2 forces,