EXAMPLE 5.4 Lifting granite and dumping dirt Blocks of granite, e...

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EXAMPLE 5.4 Lifting granite and dumping dirt Blocks of granite, each with weight W1, are being hauled up a 15° slope out Cart of a quarry (Figure 5.4). For environmental reasons, dirt is also being dumped into the quarry to fill up old holes. You have been asked to find a way to use this dirt to move the granite out more easily. You design a system that lets the dirt (weight W2, including the weight of the bucket) that drops Bucket 15° vertically into the quarry pull out a granite block on a cart with steel wheels (total weight Wi). rolling on steel rails. Ignoring the weight of the cable and friction in the pulley and wheels, determine how the weights W1 and W2 must FIGURE 5.4 be related for the system to move with constant speed. EXAMPLE 5.6 Acceleration down a hill loaded with vacationing students (total weight w) slides down a long, snow-covered slope. at The all. A hill toboggan constant angle a, and the toboggan is so well waxed that there is virtually no friction toboggan. Find slopes the toboggan's at a acceleration and the magnitude n of the normal force the hill exerts on the EXAMPLE 5.7 An air track in a physics lab Figure 5.9 shows a glider with mass 111 that moves on'a level, frictionless air track in a physics lab. It is connected by a string passing over a small frictionless pulley to a hanging weight with total mass m2. The string is light and flexible, and it doesn't stretch. Find the acceleration of each object and the tension in the string. EXAMPLE 5.8 Delivering the goods A delivery company has just unloaded a 500 N crate full of home exercise equipment in your level drive- way. You find that to get it started moving toward your garage, you have to pull with a horizontal force of magnitude 230 N. Once it "breaks loose" and starts to move, you can keep it moving at constant velocity with only 200 N of force. What are the coefficients of static and kinetic friction? 3. A man sits in a seat that is suspended from a rope. The rope passes over a pulley suspended from the ceiling, and the man holds the other end of the rope in his hands. What is the ten- sion in the rope, and what force does the seat exert on the man? Draw a free-body force diagram for the man.

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