A 500 kg air conditioner sits on the flat roof of a building. The coefficient of static friction between the roof and the air conditioner is 0.90. A massless rope attached to the air conditioner passes over a massless, frictionless pulley at the edge of the roof. In an effort to drag the air conditioner to the edge of the roof, four 100 kg students hang from the free end of the rope, but the air conditioner refuses to budge. What is the magnitude of the rope tension at the point where it is attached to the air conditioner?

(II) One 3.2-kg paint bucket is hanging by a massless cord from another 3.2-kg paint bucket, also hanging by a massless cord, as shown in Fig. 4–41.

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(a) If the buckets are at rest, what is the tension in each cord?

III) Determine a formula for the magnitude of the force F → exerted on the large block () in Fig. 4–56 so that the mass m_A does not move relative to m_C. Ignore all friction. Assume m_B does not make contact with m_C . <IMAGE>

(III) The two masses shown in Fig. 4–57 are each initially 1.8 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its 'launch' speed. Assume the mass doesn't hit the pulley or the ceiling. Ignore the mass of the cord.]

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A coffee cup on the horizontal dashboard of a car slides forward when the driver decelerates from 45 km/h to rest in 3.5 s or less, but not if she decelerates in a longer time. What is the coefficient of static friction between the cup and the dash? Assume the road and the dashboard are level (horizontal).

A 1.5-kg block rests on top of a 7.5-kg block (Fig. 4–70). The cord and pulley have negligible mass, and there is no significant friction anywhere. <IMAGE>

(b) What is the tension in the connecting cord?