A 3000 kg cable car descends down a 200-m high hill. To control its speed, it has its own brakes as well as a 2000 kg counterweight on the other side of the hill. Assume that the rolling friction of both the cable car and the counterweight are negligible.

1. Calculate the braking force necessary for the car to descend at a constant speed.
2. Calculate the car’s speed at the bottom of the hill if its brakes fail or are not engaged.

The braking force necessary for the cable car to descend at constant speed is 9800 Newtons. If the brakes were to fail, the cable car would descend with a speed of approximately 26.83 m/s at the bottom of the hill.

Explanation:

Firstly, we need to calculate the braking force necessary for the car to descend at a constant speed. The cable car and counterweight system is balanced in gravitational forces when the cable car is stationary, the gravitational force on the cable car is balanced by the gravitational force on the counterweight. When the car moves downwards, the force acting on the car is the difference between its weight (mass x gravity) and the counterweight's weight i.e.

F = (3000 kg x 9.8 m/s²) - (2000 kg x 9.8 m/s²) = 9800 Newtons.

This is the force that the brakes have to exert upwards to maintain constant speed.

Next, to calculate the car's speed at the bottom of the hill if its brakes fail or are not engaged, we use the equation for potential energy (mgh) converting to kinetic energy (1/2 mv²). However, it's the difference of the potential energy of the cable car and counterweight that becomes the kinetic energy, so

v = sqrt((2 * (3000 kg * 9.8 m/s² * 200 m - 2000 kg * 9.8 m/s² * 200 m)) / 3000 kg), which gives a result of approximately 26.83 m/s.

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