When a driver brakes an automobile, the friction between the brake drums and the brake shoes converts the car's kinetic energy to thermal energy. If a 1750-kg automobile traveling at 28 m/s comes to a halt, how much does the temperature rise in each of the four 8.0 kg iron brake drums? (The specific heat of iron is 448 J/kg · °C.)

Mv²/2 =4mcΔT

ΔT = Mv²/8mc=1750•28²/8•8•448=47.9℃

Well, let's put the temperature rise in perspective. Imagine the brake drums are having a little party and start dancing. They're getting hot, moving their iron hips! Now let's calculate how much they're heating up.

The kinetic energy of the car is converted to thermal energy, and we can use the equation:

Thermal energy = Kinetic energy

First, let's calculate the kinetic energy of the car using the formula:

Kinetic energy = (1/2) * mass * velocity^2

Kinetic energy = (1/2) * 1750 kg * (28 m/s)^2

Kinetic energy = 686,000 J

Now, since the brake drums are sharing the kinetic energy, each brake drum receives one-fourth of the total. So, each drum receives:

686,000 J / 4 = 171,500 J

Now, we can calculate the temperature rise using the equation:

Temperature rise = Thermal energy / (mass of drum * specific heat of iron)

Temperature rise = 171,500 J / (8.0 kg * 448 J/kg · °C)

Temperature rise ≈ 48.12 °C

Therefore, each of the four brake drums would heat up by approximately 48.12 °C. It's like they're enjoying a little hot iron drum party!

To calculate the temperature rise in each of the four iron brake drums, we will use the formula: Q = m × c × ΔT, where Q is the thermal energy, m is the mass, c is the specific heat, and ΔT is the change in temperature.

First, let's calculate the initial kinetic energy of the car using the formula: KE = 0.5 × m × v^2, where m is the mass of the car and v is its velocity.
KE = 0.5 × 1750 kg × (28 m/s)^2
KE = 0.5 × 1750 kg × 784 m^2/s^2
KE = 686,000 J

Since the car comes to a halt, all of the kinetic energy is converted into thermal energy. Therefore, the thermal energy can be calculated as:
Q = KE
Q = 686,000 J

Since there are four iron brake drums, we need to divide the thermal energy equally among them. So, each brake drum will receive:
Q_drum = Q / 4
Q_drum = 686,000 J / 4
Q_drum = 171,500 J

Now, let's calculate the temperature rise in each brake drum using the formula: ΔT = Q / (m × c), where ΔT is the change in temperature.
ΔT_drum = Q_drum / (m_drum × c)
ΔT_drum = 171,500 J / (8 kg × 448 J/kg · °C)
ΔT_drum = 24.08 °C

Therefore, the temperature rise in each of the four 8.0 kg iron brake drums is approximately 24.08 °C.

To calculate the temperature rise in each of the four iron brake drums, we can use the principle of conservation of energy.

First, let's find the initial kinetic energy of the car. The kinetic energy (KE) of an object is given by the formula: KE = 0.5 * mass * velocity^2.

Substituting the values:
Mass of the car (m) = 1750 kg
Velocity of the car (v) = 28 m/s

KE = 0.5 * 1750 kg * (28 m/s)^2
KE = 862,000 J

Now, the energy is transferred from the car's kinetic energy to the thermal energy of the brake drums. The amount of energy transferred can be calculated using this equation: Energy transferred = Specific heat * mass * temperature change.

Since we want to find the temperature change, we can rearrange the equation as follows: Temperature change = Energy transferred / (Specific heat * mass).

Substituting the values:
Mass of each iron brake drum = 8.0 kg
Specific heat of iron (c) = 448 J/kg · °C
Energy transferred = 862,000 J (from the car's kinetic energy)

Temperature change in each brake drum = 862,000 J / (448 J/kg · °C * 8.0 kg)
Temperature change in each brake drum ≈ 273.66 °C

So, the temperature rise in each of the four 8.0 kg iron brake drums would be approximately 273.66 °C.