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Answer :
Final answer:
To calculate the mass of the car, one would typically use the work-energy theorem and the loss of kinetic energy. However, the initial speed of the car is needed to complete this calculation. With the given data alone, the calculation cannot be completed.
Explanation:
The given problem involves calculating the mass of a car using the work-energy theorem. To find the mass of the car, we can use the loss of kinetic energy and the braking force applied over a certain time. The kinetic energy lost by the car is given as 121 kJ, which is equal to 121,000 J (since 1 kJ = 1,000 J). The force exerted by the brakes is 2,280 N. Using the relationship between work done (which in this case is the kinetic energy lost) and force, we can write:
Work done = Force × distance
Kinetic energy lost = Braking force × stopping distance
The stopping distance is not directly given, but we can calculate it from the work-energy principle that states the work done by the brakes will be equal to the change in kinetic energy.
We know that Work done = Force × distance = Change in Kinetic Energy. So, distance = Change in Kinetic Energy / Force
Now, by using the formula for kinetic energy (KE = 1/2 mv²) and solving for mass (m), we get:
m = (2 × Kinetic energy lost) / (v²)
However, we are not given the initial speed (v) of the car and cannot directly calculate the mass with the given data alone. The initial speed is required to complete the calculation for mass. Therefore, we must either assume an initial speed or obtain that information to proceed.
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