5.77 A block with mass m₁ is placed on an inclined plane with slope angle a and is connected to a hanging block with mass m₂ by a cord passing over a small, frictionless pulley (Fig. P5.74). The coef- ficient of static friction is μs, and the coefficient of kinetic friction is Mk. (a) Find the value of m₂ for which the block of mass m₁ moves up the plane at constant speed once it is set in motion. (b) Find the value of m2 for which the block of mass m₁ moves down the plane at constant speed once it is set in motion. (c) For what range of values of m₂ will the blocks remain at rest if they are released from rest?

5.78 .. DATA BIO The Flying Leap of a Flea. High-speed motion pictures (3500 frames/second) of a jumping 210 μg flea yielded the data to plot the flea's acceleration as a function of time, as shown in Fig. P5.78. (See "The Flying Leap of the Flea," by M. Rothschild et al., Scientific American, November 1973.) This flea was about 2 mm long and jumped at a nearly vertical takeoff angle. Using the graph, (a) find the initial net external force on the flea. How does it compare to the flea's weight? (b) Find the maximum net external force on this jump- ing flea. When does this maximum force occur? (c) Use the graph to find the flea's maximum speed. Figure P5.78 150 a/g 100 50 1.0 1.5 0.5 Time (ms)

5.4 ⚫ BIO Injuries to the Spinal Column. In the treatment of spine injuries, it is often necessary to provide tension along the spi- nal column to stretch the backbone. One device for doing this is the Stryker frame (Fig. E5.4a, next page). A weight W is attached to the patient (sometimes around a neck collar, Fig. E5.4b), and fric- tion between the person's body and the bed prevents sliding. (a) If the coefficient of static friction between a 78.5 kg patient's body and the bed is 0.75, what is the maximum traction force along the spi- nal column that W can provide without causing the patient to slide? (b) Under the conditions of maximum traction, what is the tension in each cable attached to the neck collar? Figure E5.4 (a) (b) W 65° 65°