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Q. 42

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 179

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Short Answer

The cable car shown in FIGURE P descends a -m-high hill. In addition to its brakes, the cable car controls its speed by pulling an counterweight up the other side of the hill. The rolling friction of both the cable car and the counterweight are negligible.

a. How much braking force does the cable car need to descend at constant speed?

b. One day the brakes fail just as the cable car leaves the top on its downward journey. What is the runaway car’s speed at the bottom of the hill?

(a) The braking force required is

(b) The car's speed at the bottom of the hill is

See the step by step solution

Step by Step Solution

Step 1: Given information (part a)

The mass of the cable car

The mass of the counterweight

Step 2: Explanation 

The force acting on the counterweight:

Sliding of the counterweight on a inclined plane

Tension acting upward

When the cable car is descending, the counterweight moves upward so the forces acting on the counterweight during the period are given by.

The force acting on the cable car

Forward sliding of the cable car on a inclined plane

Tension acting upward

Breaking force,

The braking force required is

Step 4: Given information (part b)

The mass of the cable car

The mass of the counterweight

Step 4: Explanation (part b)

The net force on the counterweight

The net force on the cable car is

Now the distance traveled by car can be calculated by using trigonometry

The car's speed at the bottom of the hill is

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