a car of mass 100 kg traveling at 72 km/hr is brought to rest by applying the brakes.assuming that the kinetic energy of the car becomes transferred to internal energy in four steel brakes drum of equal mass, fine the rise in temperature of the drums if the total is 20kg, the specific heat capacity of the steal is 450 j/kg k and the work done equal on all four drums
I want an answer,i have been going on with the question for a week now
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To find the rise in temperature of the drums, we need to calculate the kinetic energy of the car, the work done, and then use the equation for heat transfer.
1. Calculate the kinetic energy of the car:
The kinetic energy (KE) of an object can be calculated using the formula:
KE = (1/2) * mass * velocity^2
Here, the mass of the car is 100 kg and the velocity is given in km/hr.
We need to convert it to m/s by dividing it by 3.6 (because 1 km/hr = 1 m/s).
KE = (1/2) * 100 kg * (72 km/hr / 3.6)^2
2. Calculate the work done:
Work done (W) is the change in kinetic energy of the system:
W = KE
3. Find the work done on each drum:
Since the work done is equal on all four drums, each drum will receive 1/4th of the total work done:
Work done on each drum = (1/4) * W
4. Calculate the rise in temperature using the equation for heat transfer:
We can use the formula:
Q = m * c * ΔT
Here, Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
For each drum, the heat transferred is equal to the work done on the drum:
Q = Work done on each drum = (1/4) * W
Substituting Q = (1/4) * W in Q = m * c * ΔT, we get:
(1/4) * W = 20 kg * 450 J/kg K * ΔT
Solve for ΔT:
ΔT = [(1/4) * W] / [20 kg * 450 J/kg K]
You can substitute the values in the above equations to find the rise in temperature of the drums.
To find the rise in temperature of the drums, we need to calculate the work done on the drums and use the specific heat capacity of steel. Here's how you can calculate it step by step:
Step 1: Calculate the initial kinetic energy of the car.
The formula to calculate kinetic energy is:
Kinetic energy = 1/2 * Mass * Velocity^2
In this case, the mass of the car is given as 100 kg and the velocity is given as 72 km/hr. However, we need to convert the velocity from km/hr to m/s:
72 km/hr = 72 * 1000 m/3600 s
= 20 m/s (approximately)
So the initial kinetic energy of the car can be calculated as follows:
Initial Kinetic Energy = 1/2 * Mass * Velocity^2
= 1/2 * 100 kg * (20 m/s)^2
= 1/2 * 100 kg * 400 m^2/s^2
= 20,000 J
Step 2: Calculate the work done on the drums.
Since the work done on all four drums is equal, we can divide the initial kinetic energy by four to get the work done on each drum:
Work Done on Each Drum = Initial Kinetic Energy / Number of Drums
= 20,000 J / 4
= 5,000 J
Step 3: Calculate the heat energy transferred to the drums.
As per the law of conservation of energy, the kinetic energy of the car is transferred as heat energy to the drums. Therefore, the heat energy transferred to the drums is equal to the work done on each drum.
Heat Energy Transferred to the Drums = Work Done on Each Drum
= 5,000 J
Step 4: Calculate the rise in temperature of the drums.
The rise in temperature can be found using the formula:
Heat Energy = Mass * Specific Heat Capacity * Rise in Temperature
We are given the mass of the drums as 20 kg and the specific heat capacity of steel as 450 J/kg K. Plugging these values into the formula, we can solve for the rise in temperature:
5,000 J = 20 kg * 450 J/kg K * Rise in Temperature
Rise in Temperature = 5,000 J / (20 kg * 450 J/kg K)
= 0.556 °C (approximately)
Therefore, the rise in temperature of the steel drums would be approximately 0.556 °C.