6. Intro to Forces (Dynamics)

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. What is the tension in the connecting cord?

A window washer pulls herself upward using the bucket–pulley apparatus shown in Fig. 4–40. If she increases this force by 15%, what will her acceleration be? The mass of the person plus the bucket is 78 kg.

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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.

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. 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) Determine a formula for the magnitude of the force $\overrightarrow{F}$ exerted on the large block (m_C) 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.

FIGURE EX7.17 shows two 1.0 kg blocks connected by a rope. A second rope hangs beneath the lower block. Both ropes have a mass of 250 g. The entire assembly is accelerated upward at 3.0 m/s² by force F. What is the tension at the top end of rope 1?

The double Atwood machine shown in Fig. 4–55 has frictionless, massless pulleys and cords. Determine the acceleration of masses m_A, m_B, and m_C.

The 1.0 kg block in FIGURE EX7.23 is tied to the wall with a rope. It sits on top of the 2.0 kg block. The lower block is pulled to the right with a tension force of 20 N. The coefficient of kinetic friction at both the lower and upper surfaces of the 2.0 kg block is μ_k = 0.40. What is the tension in the rope attached to the wall?

A rope of length L and mass m is suspended from the ceiling. Find an expression for the tension in the rope at position y, measured upward from the free end of the rope.

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

What minimum force F is needed to lift a piano (mass M) using the pulley apparatus shown in Fig. 4–64? Determine the tension in each section of rope: F_T1, F_T2, F_T3 and F_T4. Assume pulleys are massless and frictionless, and that ropes are massless.