A 575-g steel hammer, with a specific heat capacity of 460 J/kg°C hits a titanium block at 14 m/s. If all the kinetic energy of the hammer was converted into thermal energy of the hammer.
What is the increase in temperature of the hammer?
0.21 °C
0.53 °C
1.2 °C
1.8
°C
Answer: 1.2 °C
To find the increase in temperature of the hammer when all the kinetic energy is converted into thermal energy, we can use the equation:
ΔQ = m × c × ΔT
where:
ΔQ is the change in thermal energy
m is the mass of the hammer
c is the specific heat capacity of the hammer
ΔT is the change in temperature
We can first calculate the change in thermal energy using the formula:
ΔQ = KE
where:
KE is the kinetic energy of the hammer, which can be calculated using the formula:
KE = 0.5 × m × v^2
where:
m is the mass of the hammer
v is the velocity of the hammer
Given:
Mass of the hammer (m) = 575 g = 0.575 kg
Specific heat capacity of the hammer (c) = 460 J/kg°C
Velocity of the hammer (v) = 14 m/s
Calculating the kinetic energy (KE):
KE = 0.5 × m × v^2
KE = 0.5 × 0.575 kg × (14 m/s)^2
KE = 56.07 J
Now, we can substitute the value of ΔQ into the equation and solve for ΔT:
ΔQ = m × c × ΔT
56.07 J = 0.575 kg × 460 J/kg°C × ΔT
Solving for ΔT:
ΔT = 56.07 J / (0.575 kg × 460 J/kg°C)
ΔT ≈ 0.216 °C
So, the increase in temperature of the hammer when all the kinetic energy is converted into thermal energy is approximately 0.216 °C.
To find the increase in temperature of the hammer, we can use the equation:
Q = mcΔT
Where:
Q is the thermal energy gained by the hammer,
m is the mass of the hammer,
c is the specific heat capacity of the hammer, and
ΔT is the change in temperature.
First, let's calculate the kinetic energy of the hammer:
KE = 0.5mv^2
Where:
m is the mass of the hammer, and
v is the velocity of the hammer.
KE = 0.5 * 0.575 kg * (14 m/s)^2
KE = 0.5 * 0.575 kg * 196 m^2/s^2
KE = 56.35 J
Since all the kinetic energy is converted into thermal energy:
Q = KE
Q = 56.35 J
Now, let's solve for ΔT:
Q = mcΔT
56.35 J = 0.575 kg * 460 J/kg°C * ΔT
ΔT = 56.35 J / (0.575 kg * 460 J/kg°C)
ΔT ≈ 0.217 °C
Therefore, the increase in temperature of the hammer is approximately 0.217 °C, which is closest to 0.21 °C.