Two cars collide head on while each is travelling at 80 km/hr. Suppose all of their
kinetic energy is transformed into thermal energy. What is the temperature increase
of each car? [You may assume that the specific heat capacity of each car is that of
iron, 449 J kg-1K-1.]
Divide the initial total kinetic energy (M V^2) by the heat capacity (2*M*C). M is the mass per car.
To compute total KE in Joules, note than you must first convert 80 km/h to 22.22 m/s. You must include a factor of 2 because there are two cars
Leave the mass as an unknown factor, M. It will cancel out
Then
delta T = V^2/(2 C)
where C is the specific heat
I get a T rise of 0.55 C (or K)
Well, if those cars are colliding head-on at 80 km/hr, I think they'll have more than just a temperature increase to worry about. They might need a whole new set of wheels, or maybe even a new driver's license! But let's focus on the temperature for now.
First, we need to convert the speed from km/hr to m/s, because that's how the specific heat capacity of iron is typically measured. So, 80 km/hr is about 22.22 m/s.
Now, let's calculate the kinetic energy of each car. The formula for kinetic energy is KE = 1/2 * mass * velocity^2. Since we don't know the mass of the cars, let's just assume they are the same and call it "m".
The kinetic energy of each car would then be KE = 1/2 * m * (22.22)^2.
Now, since all of the kinetic energy is transformed into thermal energy, we can calculate the temperature increase using the formula ΔQ = mcΔT, where ΔQ is the thermal energy, m is the mass, c is the specific heat capacity, and ΔT is the temperature change.
To find the temperature increase, we need to rearrange the formula to solve for ΔT:
ΔT = ΔQ / (mc)
Since all the kinetic energy is converted into thermal energy, ΔQ would be equal to the initial kinetic energy. So:
ΔT = KE / (mc)
Plugging in the values we already calculated:
ΔT = (1/2 * m * (22.22)^2) / (m * 449)
Simplifying this equation, you'll find that the mass cancels out:
ΔT = (1/2 * 22.22^2) / 449
Now we can calculate:
ΔT ≈ 0.487 °C
So, each car would experience an increase in temperature of around 0.487 degrees Celsius. But hey, it's always good to drive carefully and avoid head-on collisions, instead of worrying about temperature changes!
To calculate the temperature increase of each car, we need to find the change in thermal energy.
The formula for the kinetic energy is:
KE = 1/2 * m * v^2
where KE is the kinetic energy, m is the mass of the car, and v is the velocity.
Given that the cars are traveling at 80 km/hr, we need to convert this to meters per second (m/s).
1 km/hr is equal to 0.2778 m/s.
So, 80 km/hr = 80 * 0.2778 = 22.22 m/s.
Assuming both cars have the same mass, let's say m = m1 = m2.
The total kinetic energy for both cars combined is:
KE_total = 1/2 * (m1 + m2) * v^2
Since both cars have the same mass, we can rewrite this as:
KE_total = m * v^2
Now, let's find the kinetic energy for each car individually, which is half of the total kinetic energy:
KE_car = 1/2 * KE_total
Now, let's calculate the thermal energy using the formula:
Thermal_energy = KE_car
Finally, we can calculate the temperature increase using the formula:
Temperature_increase = thermal_energy / (m * specific_heat_capacity)
Given that the specific heat capacity of iron is 449 J kg^-1 K^-1, we can substitute this value into the formula.
Temperature_increase = thermal_energy / (m * 449)
Please provide the mass of each car so that we can proceed with the calculations.
To determine the temperature increase of each car, we need to calculate the thermal energy released in the collision. The thermal energy can be calculated using the formula:
Thermal energy (Q) = Kinetic energy (KE)
The kinetic energy is given by:
Kinetic energy (KE) = 0.5 × mass × velocity^2
Given that both cars are traveling at 80 km/hr and the mass of each car is not provided, we will need to make some assumptions. Let's assume the mass of each car is 1000 kg.
Converting the velocity from km/hr to m/s, we have:
Velocity = 80 km/hr × (1000 m/1 km) × (1 hr/3600 s) = 22.22 m/s
Now, we can calculate the kinetic energy of each car:
KE = 0.5 × 1000 kg × (22.22 m/s)^2 = 246,210 J
Since the collision results in the total kinetic energy being transformed into thermal energy, the thermal energy released is equal to the kinetic energy:
Q = 246,210 J
Now, let's calculate the temperature increase of each car using the specific heat capacity of iron (449 J kg^(-1)K^(-1)):
Temperature increase (ΔT) = Q / (mass × specific heat capacity)
For each car:
ΔT = 246,210 J / (1000 kg × 449 J kg^(-1)K^(-1)) = 0.547 K
Therefore, the temperature increase of each car is approximately 0.547 K.