Figure P5.62 5.62 - In Fig. P5.62 a worker lifts a weight w by pulling down on a rope with a force F. The upper pulley is attached to the ceiling by a chain, and the lower pulley is attached to the weight by another chain. Draw one or more free-body diagrams to find the tension in each chain and the magni- tude of F, in terms of w, if the weight is lifted at constant speed. Assume that the rope, pulleys, and chains have negligible weights.

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Jarrod RobelLv2

28 Jul 2018

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5.37. Two crates connected by a rope lie on a horizontal sur- face (Fig. E5.37). Crate A has mass mA, and crate B has mass mp. The coefficient of kinetic friction between each crate and the sur- face is plk. The crates are pulled to the right at constant velocity by a horizontal force F. Draw one or more free-body diagrams to calculate the following in terms of ma, mg, and up: (a) the magni- tude of F and (b) the tension in the rope connecting the blocks. Figure E5.37

This problem introduces the concept of tension. The example is a rope, oriented vertically, that is being pulled from both ends. Let F_u and F_d (with u for up and d for down) represent the magnitude of the forces acting on the top and bottom of the rope, respectively. Assume that the rope is massless so that its weight is negligible compared with the tension. (This is not a ridiculous approximation-modern rope material such as Kevlar can carry tensions thousands of times greater than the weight of tens of meters of such rope.)

Consider the three sections of rope labeled a, b, and c in the figure.

At point 1, a downward force of magnitude F_ad acts on section a.
At point 1, an upward force of magnitude F_bu acts on section b.
At point 1, the tension in the rope is T₁.
At point 2, a downward force of magnitude F_bd acts on section b.
At point 2, an upward force of magnitude F_cu acts on section c.
At point 2, the tension in the rope is T₂.

(A) What is the magnitude F_ad of the downward force on section a?

(B) What is the magnitude F_bu of the upward force on section b?

(C) The magnitude of the upward force on c, F_cu, and the magnitude of the downward force on b, F_bd, are equal because of which of Newton's laws?

(D) The magnitude of the force F_bu is ______ F_bd.

(E) Now consider the forces on the ends of the rope. What is the relationship between the magnitudes of these two forces?

(a) F_u > F_d

(b) F_u = F_d

(F) The ends of a massless rope are attached to two stationary objects (e.g., two trees or two cars) so that the rope makes a straight line. For this situation, which of the following statements are true?

(a) The tension in the rope is everywhere the same.

(b) The magnitudes of the forces exerted on the two objects by the rope are the same.

(d) The forces exerted on the two objects by the rope must be in the direction of the rope.

ambergiraffe181

The large quadriceps muscle in the upper leg terminates at its lower end in a tendon attached to the upper end of the tibia (Fig. P8.27a). The forces on the lower leg when the leg is extended are modeled as in Figure P8.27b, where vector T is the force of tension in the tendon, vector w is the force of gravity acting on the lower leg, and vector F is the force of gravity acting on the foot. Find vector T when the tendon is at an angle of 25.0° with the tibia, assuming that ? = 40.0 N, F = 13.5 N, and the leg is extended at an angle ? of 40.0° with the vertical. Assume that the center of gravity of the lower leg is at its center, and that the tendon attaches to the lower leg at a point one fifth of the way down the leg.

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