Help......A 1.0kg metal head of a geology hammer stikes a solid rock withy a velocity of 5.0m/s. Assuming all the energy is retained by the hammer head, how much will its temperature increase? (C
head= 0.11kcal/kgCdegrees) I don't comprehend any of this!
kinetic energy in hammer= heat in hammer
1/2 m v^2= m*specificheatSteel*deltatemp
change in temperature= (1/2mv^2)/(m*specifheat)
change in temperature= v^2/(2*specificheat)
change in temperature: (5m/s)^2 /2*920
Did you change kcal to joules? .11kcal=920Joules check that.
now I'm really lost.....please explain?
To solve this problem, we need to understand a few concepts:
1. Conservation of Energy: The Law of Conservation of Energy states that energy cannot be created or destroyed, only transferred or converted from one form to another.
2. Kinetic Energy: Kinetic energy is the energy possessed by an object due to its motion. The formula for kinetic energy is given by KE = 0.5 * m * v^2, where m is the mass of the object and v is its velocity.
3. Specific Heat Capacity: Specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or one Kelvin). It is represented by the symbol C and measured in units of energy per unit mass per degree Celsius (e.g., J/kg°C or kcal/kg°C).
Now, let's calculate the increase in temperature of the hammer head after striking the rock:
Step 1: Calculate the initial kinetic energy of the hammer head.
KE = 0.5 * m * v^2
KE = 0.5 * 1.0 kg * (5.0 m/s)^2
KE = 12.5 J
Step 2: Convert the kinetic energy to calories (1 J = 0.239 kcal).
Energy in kcal = 12.5 J * 0.239 kcal/J
Energy in kcal = 2.9875 kcal
Step 3: Calculate the temperature increase using the specific heat capacity.
Temperature increase = Energy / (m * C)
Temperature increase = 2.9875 kcal / (1.0 kg * 0.11 kcal/kg°C)
Temperature increase = 27.159 °C
Therefore, the hammer head's temperature will increase by approximately 27.159 °C.
Note: Make sure to use consistent units throughout the calculation. The given specific heat capacity (C) is in kcal/kg°C, so we converted the energy to kcal to match the units for the calculation.