A 1.0 kg metal head of a geology hammer strikes a solid rock with a velocity of 5.0 m/s. Assuming all the energy is retained by the hammer head, how much will its temperature increase?
(1/2)MV^2 = M C (delta T)
Solve for the temperaure change: delta T.
C is the specific heat of the metal head. M cancels out and is not needed.
delta T = V^2/(2 C)
C should have units of Joules/(kg C). Use a C value for stainless steel. They should have told you what the geology hammer head is made of.
Well, let's see. If a geology hammer head strikes a rock and retains all the energy, it's going to get hot! We can calculate the temperature increase using the principle of conservation of energy.
First, we need to determine the initial kinetic energy of the hammer head. The formula for kinetic energy is KE = 0.5 * mass * velocity^2. Plugging in the values, we get KE = 0.5 * 1.0 kg * (5.0 m/s)^2 = 12.5 J (joules).
Now, let's assume all this energy is converted into heat. We can use the formula Q = mcΔT, where Q is the amount of heat transferred, m is the mass of the hammer head, c is the specific heat capacity of the metal, and ΔT is the change in temperature.
Since we're looking for the change in temperature, we can rearrange the equation to solve for ΔT: ΔT = Q / (mc).
We don't have the specific heat capacity of the metal here, so let's just assume it's a friendly metal that doesn't mind getting heated up. In that case, we can use an average value of around 500 J/(kg·°C) for most metals.
Plugging in the values, we get ΔT = 12.5 J / (1.0 kg * 500 J/(kg·°C)) ≈ 0.025 °C.
So, the temperature of the hammer head would increase by approximately 0.025 degrees Celsius. Well, that's not much of a temperature change. The hammer head might not even break a sweat!
To determine the increase in temperature of the hammer head, we need to use the concept of conservation of energy. When the hammer strikes the rock, the kinetic energy of the hammer head is converted into internal energy, causing its temperature to rise.
The increase in temperature can be calculated using the equation:
Q = mcΔT
Where:
Q is the heat energy gained by the hammer head (in joules)
m is the mass of the hammer head (in kilograms)
c is the specific heat capacity of the material (in J/kg·°C)
ΔT is the change in temperature (in °C)
First, we need to determine the heat energy gained by the hammer head. This can be calculated using the equation:
Q = 0.5mv^2
Where:
m is the mass of the hammer head (in kilograms)
v is the velocity of the hammer head (in meters per second)
Given:
m = 1.0 kg (mass of the hammer head)
v = 5.0 m/s (velocity of the hammer head)
Q = 0.5 * 1.0 kg * (5.0 m/s)^2
Q = 0.5 * 1.0 kg * 25.0 m^2/s^2
Q = 12.5 joules
Now, we need to determine the specific heat capacity of the material. Let's assume the hammer head is made of steel. The specific heat capacity of steel is approximately 450 J/kg·°C.
c = 450 J/kg·°C
Finally, we can calculate the change in temperature using the equation:
ΔT = Q / (mc)
ΔT = 12.5 J / (1.0 kg * 450 J/kg·°C)
ΔT ≈ 0.0278 °C
Therefore, the temperature of the hammer head will increase by approximately 0.0278 °C.
1/2 MV^2 is the kinetic energy of the hammer. V is the velocity which is given.
MC delta T is the heat of a compound (m is mass but it cancels, C is the specific heat which you will need to look up AND you need to know what material the hammer is) and delta T is what you solve for. Only one unknown (delta T) IF you know the hammer is made of iron or whatever.