An aluminum block slides along a horizontal surface. The block has an initial speed of 11.6 m/s and an initial temperature of 10.7°C. The block eventually slides to rest due to friction. Assuming all the initial kinetic energy is converted to heat energy and all this energy stays in the block, what is the final temperature of the block?

Question

An aluminum block slides along a horizontal surface. The block has an initial speed of 11.6 m/s and an initial temperature of 10.7°C. The block eventually slides to rest due to friction. Assuming all the initial kinetic energy is converted to heat energy and all this energy stays in the block, what is the final temperature of the block?

Answer 1

To find the final temperature of the block, we need to use the principle of energy conservation. The initial kinetic energy of the block is converted into heat energy due to friction, which causes the block to come to rest.

The formula for kinetic energy is given by K = (1/2)mv^2, where K is the kinetic energy, m is the mass of the block, and v is the initial velocity of the block.

First, we need to calculate the mass of the aluminum block. This requires knowing the density of aluminum, which is 2.7 g/cm³, or 2700 kg/m³.

Let's assume the dimensions of the block are known, such as length, width, and height. Then, the volume of the block can be determined by multiplying these dimensions.

Next, we can calculate the mass of the block by multiplying the volume by the density.

Once we have the mass of the block, we can use the formula for kinetic energy to find its initial value. From the given information, we know the initial velocity, so we plug in the values to calculate the initial kinetic energy.

Now, since all the initial kinetic energy is converted into heat energy, we can equate the initial kinetic energy to the heat energy.

The formula for heat energy is given by Q = mcΔT, where Q is the heat energy, m is the mass of the block, c is the specific heat of aluminum (0.897 J/g°C or 897 J/kg°C), and ΔT is the change in temperature.

Rearranging the formula, we can solve for ΔT:

ΔT = Q / (mc)

Substituting the initial kinetic energy for Q and the calculated mass for m, we can find the change in temperature.

To find the final temperature, we add the change in temperature (ΔT) to the initial temperature (10.7°C).

Finally, this gives us the value of the final temperature of the aluminum block.

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To find the final temperature of the block, we need to use the principle of energy conservation. The initial kinetic energy of the block is converted into heat energy due to friction, which causes the block to come to rest.