a snow ball at 0 degrees celsius is thrown against a brick wall. if all the kinetic energy of the snowball turns to heat upon striking the wall, how fast must you throw the snowball to cause it to melt completely?
To determine the speed at which the snowball must be thrown to cause it to melt completely upon hitting the wall, we need to consider the energy involved in the process. The kinetic energy of the snowball is converted into heat energy upon impact. To calculate the required speed, we can use the energy conservation principle.
First, let's consider the energy of the snowball before it hits the wall. The kinetic energy (KE) is given by the formula:
KE = 1/2 * mass * velocity^2
Next, we need to consider the energy required to melt the snowball. This is given by the formula:
Q = mass * heat of fusion
Where Q is the heat energy and the heat of fusion is the amount of heat required to change one gram of a substance from solid to liquid (for water, it is 334 joules/gram).
Now, equating the kinetic energy to the heat energy required to melt the snowball, we have:
1/2 * mass * velocity^2 = mass * heat of fusion
Mass cancels out from both sides of the equation, giving us:
1/2 * velocity^2 = heat of fusion
Since the brick wall does not contribute or absorb any significant energy, we just need to consider the heat of fusion.
Plugging in the heat of fusion for snow (334 J/g), we find:
1/2 * velocity^2 = 334
Now solve for velocity:
velocity^2 = 2 * 334
velocity^2 = 668
velocity = sqrt(668)
velocity ≈ 25.86 m/s (rounded to two decimal places)
Therefore, to cause the snowball to melt completely upon impact with the wall, you would need to throw it at a speed of approximately 25.86 m/s.