Question

A 1000 kg car with a speed of 90 km/h brakes to a stop. How many calories of heat are generated by the brakes as a result?

Answer 1

To determine the heat generated by the brakes, the car's kinetic energy at 90 km/h is converted to Joules and then to calories, resulting in approximately 74,653.1 calories of heat.

Step-by-step explanation:

To calculate how many calories of heat are generated by a 1000 kg car braking to a stop from a speed of 90 km/h, we first need to convert the speed to meters per second (m/s). The conversion factor is 1 km/h = 0.27778 m/s, so (90 km/h)(0.27778 m/s per km/h) = 25 m/s. Using the formula for kinetic energy, E_k = 0.5 × m × v^2, we find that the energy dissipated is (0.5)(1000 kg)(25 m/s)^2 = 312500 J.

Since there are 4.184 Joules in one calorie, the amount of heat generated in calories is 312500 J / 4.184 J/cal = 74653.1 calories.

Answer 2

Based on the question, we are going to assume that the energy generated by brakes is going to transform into heat.

`\begin{gathered} E=Q \\ E=(mv^2)/(2) \\ E=(1000kg\cdot((90)/(3.6)m/s)^2)/(2) \\ E=312500J \\ \end{gathered}`

Now we have to transform J into calories

`312500J=74689.3\text{ }cal`