A 2.5 kg block of ice at a temperature of 0.0 degrees Celcius and an initial speed of 5.7 m/s slides across a level floor. If 3.3 x 10^5 J are required to melt 1.0 kg of ice, how much ice melts, assuming that the initial kinetic energy of the ice block is entirely converted to the ice's internal energy?
(Our teacher doesn't teach us, plus I'm not really geared towards physics. Any help provided would be appreciated.)
I almost forgot to thank you :)
Well, it seems like this block of ice is having quite the adventure on that level floor! Let's see if we can help it out with some physics.
First of all, we need to calculate the initial kinetic energy of the ice block. Kinetic energy is given by the formula KE = 1/2 * mass * velocity^2.
Plugging in the values, we get:
KE = 1/2 * 2.5 kg * (5.7 m/s)^2
Calculating that, we find the initial kinetic energy of the ice block.
Now, it's given that this initial kinetic energy is entirely converted to the ice's internal energy. We know that 3.3 x 10^5 J of energy is required to melt 1.0 kg of ice. So, we can find out how much ice melts by dividing the initial kinetic energy by the energy required to melt 1.0 kg of ice.
And voila! That will give you the amount of ice that melts. Remember to check your units, so you don't end up with melted ice cream instead!
To solve this problem, we need to consider the conservation of energy. The initial kinetic energy of the ice block will be converted into the internal energy of the ice as it melts.
Step 1: Find the initial kinetic energy of the ice block.
The formula to calculate the kinetic energy is:
Kinetic energy = (1/2) * mass * velocity^2
Given:
Mass of the ice block (m) = 2.5 kg
Initial speed of the ice block (v) = 5.7 m/s
Using the formula, the initial kinetic energy (KE_initial) can be calculated as follows:
KE_initial = (1/2) * 2.5 kg * (5.7 m/s)^2
Step 2: Calculate the amount of ice that melts using the conservation of energy.
The heat energy required to melt a certain amount of ice can be calculated using the equation:
Heat energy (Q) = mass of ice melted * heat of fusion
Given:
Heat energy required to melt 1 kg of ice (Q_fusion) = 3.3 x 10^5 J
Since the initial kinetic energy is entirely converted to the ice's internal energy, we can equate the initial kinetic energy to the heat energy required to melt the ice:
KE_initial = Q_fusion * mass of ice melted
Rearranging the equation, we get:
Mass of ice melted = KE_initial / Q_fusion
Substituting the values, we have:
Mass of ice melted = [(1/2) * 2.5 kg * (5.7 m/s)^2] / (3.3 x 10^5 J)
Now, we can calculate the value using a calculator:
Mass of ice melted = (1/2) * 2.5 kg * (5.7 m/s)^2 / (3.3 x 10^5 J)
Once you evaluate the above expression, you will find the mass of ice melted.
To solve this problem, we need to analyze the energy transfer that occurs when the ice block slides across the floor.
First, let's calculate the initial kinetic energy (KE) of the ice block:
KE = 1/2 * mass * velocity^2
Given: mass = 2.5 kg, velocity = 5.7 m/s
KE = 1/2 * 2.5 kg * (5.7 m/s)^2
= 1/2 * 2.5 kg * 32.49 m^2/s^2
= 40.6125 J
Next, we need to determine how much ice can melt with the energy of 40.6125 J. We'll use the given energy required to melt 1.0 kg of ice, which is 3.3 x 10^5 J.
Let's assume that the energy transferred due to sliding friction is entirely converted into the ice's internal energy, which causes it to melt.
The amount of ice melted can be calculated using the formula:
amount of ice melted = energy transferred / energy required to melt 1 kg of ice
amount of ice melted = 40.6125 J / 3.3 x 10^5 J
To simplify the calculation, we can divide both numerator and denominator by 5.
amount of ice melted = (40.6125 J / 5) / (3.3 x 10^5 J / 5)
= 8.1225 J / (6.6 x 10^4 J)
= 1.231 x 10^(-4) kg
Therefore, approximately 1.231 x 10^(-4) kg of ice will melt when the initial kinetic energy of the ice block is entirely converted to the ice's internal energy.
Note: This assumes that all the energy is transferred to the ice and none is lost to other factors. In real-world scenarios, there might be some energy loss due to factors like heat dissipation.
What does your teacher do?
Compute the initial kinetic energy (KE) of the ice using
KE = (1/2) M V^2
You should get 40.6 Joules
Divide that by 3.3*10^5 J/kg to get the number of kg's that melt.
Very little ice melts compared to the mass of the block. No energy goes into raising the temperature because it stays at 0C until it all melts.