a car of mass 1360 kg descends from a hill of height 86 m at a constant speed of 20 km/h. assuming that all the potential/kinetic energy of the car goes into heat in the brakes, find the rise in temperature of the brakes (use the heat capacity (C) of the brakes to be 16kJ/C and ignore any heat losses to the surroundings
To calculate the rise in temperature of the brakes, we need to determine the change in potential energy and kinetic energy of the car.
1. Change in Potential Energy:
The potential energy change can be calculated using the formula:
Potential Energy = mass x acceleration due to gravity x height
The mass of the car is 1360 kg, the acceleration due to gravity is approximately 9.81 m/s^2, and the height of the hill is 86 m. Substituting these values into the formula, we get:
Potential Energy = 1360 kg x 9.81 m/s^2 x 86 m
2. Change in Kinetic Energy:
Since the car is descending from the hill at a constant speed, there is no change in kinetic energy.
Therefore, the total energy converted into heat is equal to the change in potential energy of the car.
3. Conversion to heat:
The total energy converted to heat can be calculated using the formula:
Energy = mass x heat capacity x change in temperature
Here, the mass and heat capacity are given as 1360 kg and 16 kJ/C, respectively.
4. Solve for change in temperature:
Rearrange the formula to solve for the change in temperature:
Change in Temperature = Energy / (mass x heat capacity)
Substituting the known values, we get:
Change in Temperature = (Potential Energy) / (mass x heat capacity)
Calculate the potential energy using the values mentioned earlier, then substitute that value along with the mass and heat capacity.
Finally, calculate the change in temperature to find the rise in temperature of the brakes.
its 71.7 K
that other answer of 73.1 is wrong
To find the rise in temperature of the brakes, we need to calculate the amount of heat generated by the conversion of potential and kinetic energy.
First, let's calculate the gravitational potential energy (GPE) of the car at the top of the hill using the formula:
GPE = mgh
where
m = mass of the car = 1360 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height of the hill = 86 m
GPE = 1360 kg * 9.8 m/s^2 * 86 m
GPE = 1142864 J
Next, let's convert the speed from km/h to m/s:
Speed = 20 km/h = (20 * 1000) m/ (3600) s
Speed = 5.56 m/s
The kinetic energy (KE) of the car can be calculated using the formula:
KE = 0.5 * m * v^2
where
m = mass of the car = 1360 kg
v = velocity of the car = 5.56 m/s
KE = 0.5 * 1360 kg * (5.56 m/s)^2
KE = 21469.632 J
The total energy converted into heat can be calculated by adding the GPE and KE:
Total Energy = GPE + KE
Total Energy = 1142864 J + 21469.632 J
Total Energy = 1164333.632 J
Finally, we can calculate the rise in temperature of the brakes using the heat capacity formula:
q = m * C * ΔT
where
q = heat generated in Joules
m = mass of the brakes (assumed to be the same as the car, 1360 kg)
C = heat capacity of the brakes = 16 kJ/C = 16000 J/C
ΔT = rise in temperature (unknown)
Rearranging the formula, we can solve for ΔT:
ΔT = q / (m * C)
ΔT = 1164333.632 J / (1360 kg * 16000 J/C)
ΔT ≈ 4.80 °C
Therefore, the rise in temperature of the brakes is approximately 4.80 °C.
Q=c*delta T
c=16
q=potential energy
potential energy=mgh
h=86
g=10
m=1360
Q/c = delta T
Delta T= 73.1 K