6. Intro to Forces (Dynamics)

(II) A 75-kg petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 62 kg. How might the thief use this 'rope' to escape? Give a quantitative answer.

(II) A window washer pulls herself upward using the bucket–pulley apparatus shown in Fig. 4–40.

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(b) If she increases this force by 15%, what will her acceleration be? The mass of the person plus the bucket is 78 kg.

(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?

(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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(b) If the two buckets are pulled upward with an acceleration of 1.45m/s² by the upper cord, calculate the tension in each cord.

(III) The double Atwood machine shown in Fig. 4–55 has frictionless, massless pulleys and cords. <IMAGE>

Determine (a) the acceleration of masses m_A,m_B ,and m_C.

(a) What minimum force F is needed to lift a piano (mass M) using the pulley apparatus shown in Fig. 4–64? <IMAGE>