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?

Question

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

Answer 1

°C

Answer: 1.2 °C

Answer 2

To find the increase in temperature of the hammer, we need to calculate the thermal energy generated when its kinetic energy is converted. We can use the formula:

Thermal energy (Q) = mass (m) × specific heat capacity (c) × change in temperature (ΔT)

First, let's find the kinetic energy (KE) of the hammer using the formula:

Kinetic energy (KE) = 0.5 × mass (m) × velocity²

Given:
Mass of the hammer (m) = 575 g = 0.575 kg
Velocity (v) = 14 m/s

Substituting the values:
KE = 0.5 × 0.575 kg × (14 m/s)²
KE = 0.5 × 0.575 kg × 196 m²/s²
KE ≈ 64.52 J

Since all of this kinetic energy is converted to thermal energy, we can write:

Thermal energy (Q) = Kinetic energy (KE)

Now, let's rearrange the thermal energy formula and solve for the change in temperature (ΔT):

ΔT = Q / (m × c)

Given:
Specific heat capacity (c) = 460 J/kg°C

Substituting the values:
ΔT = 64.52 J / (0.575 kg × 460 J/kg°C)
ΔT ≈ 0.21 °C

Therefore, the increase in temperature of the hammer is approximately 0.21°C.

Answer 3

To calculate the increase in temperature of the hammer, we need to determine the amount of thermal energy gained by the hammer, using the equation:

Thermal energy = mass × specific heat capacity × temperature change

Given:
Mass of the hammer (m) = 0.575 kg
Specific heat capacity of steel (c) = 460 J/kg°C
Initial velocity of the hammer (v) = 14 m/s

First, we need to calculate the kinetic energy of the hammer using:
Kinetic energy = 0.5 × mass × velocity^2

Kinetic energy = 0.5 × 0.575 kg × (14 m/s)^2
Kinetic energy = 113.17 J

Since all the kinetic energy is converted into thermal energy, the amount of thermal energy gained by the hammer is equal to the kinetic energy:

Thermal energy = 113.17 J

Next, we can rearrange the equation for thermal energy to solve for the temperature change:

Temperature change = Thermal energy / (mass × specific heat capacity)

Temperature change = 113.17 J / (0.575 kg × 460 J/kg°C)
Temperature change = 0.5475°C

Therefore, the increase in temperature of the hammer is approximately 0.55°C.