6. Intro to Forces (Dynamics)

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?

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?

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 2.0-m-long, 500 g rope pulls a 10 kg block of ice across a horizontal, frictionless surface. The block accelerates at 2.0 m/s². How much force pulls forward on he rope? Assume that the rope is perfectly horizontal.

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 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?

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.

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.

(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.

The double Atwood machine shown in Fig. 4–55 has frictionless, massless pulleys and cords. Determine the tensions F_TA and F_TC in the cords.