A 1.4-kg copper block is given an initial speed of 2.0 m/s on a rough horizontal surface. Because of friction, the block finally comes to rest.
(a) If the block absorbs 85% of its initial kinetic energy as internal energy, calculate its increase in temperature.
0.85*(1/2)*M*V^2 = M C*(delta T)
C is the specific heat of copper.
You will have to look it up. You will need it in units of Joule/(kg*degC)
The copper mass M cancels out.
Solve for the temerature rise, delta T
delta T = (0.425)V^2/C
To solve this problem, we need to make use of the principle of conservation of energy.
Step 1: Calculate the initial kinetic energy (KE_initial) of the copper block using the formula:
KE_initial = 0.5 * mass * velocity^2
Given:
Mass (m) = 1.4 kg
Initial velocity (v_initial) = 2.0 m/s
Plugging in the values:
KE_initial = 0.5 * 1.4 kg * (2.0 m/s)^2
= 0.5 * 1.4 kg * 4.0 m^2/s^2
= 2.8 J
Step 2: Calculate the energy absorbed as internal energy (E_absorbed) by multiplying the initial kinetic energy by the absorption factor (85% or 0.85).
E_absorbed = KE_initial * absorption factor
= 2.8 J * 0.85
= 2.38 J
Step 3: Calculate the increase in temperature (ΔT) using the relationship:
ΔT = E_absorbed / (mass * specific heat capacity)
The specific heat capacity of copper is approximately 386 J/kg°C.
Given:
Specific heat capacity (c) = 386 J/kg°C
Plugging in the values:
ΔT = 2.38 J / (1.4 kg * 386 J/kg°C)
Simplifying the equation:
ΔT ≈ 0.0044 °C
Therefore, the increase in temperature of the copper block is approximately 0.0044 °C.