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Figure P10.79

80.A thin rod of mass 0.630 kg and length 1.24 m is at rest, hanging vertically from a strong fixed hinge at its top end.  Suddenly a horizontal impulsive force is applied to it.  (a) Suppose the force acts at the bottom end of the rod.  Find the acceleration of its center of mass and the horizontal force the hinge exerts.  (b) Suppose the force acts at the midpoint of the rod.  Find the acceleration of this point and the horizontal hinge reaction.  (c) Where can the impulse be applied so that the hinge will exert no horizontal force?  This point is called the center of percussion.

81.A bowler releases a bowling ball with no spin, sending it sliding straight down the alley toward the pins.  The ball continues to slide for a distance of what order of magnitude, before its motion becomes rolling without slipping?  State the quantities you take as data, the values you measure or estimate for them, and your reasoning.

82.Following Thanksgiving dinner your uncle falls into a deep sleep, sitting straight up facing the television set.  A naughty grandchild balances a small spherical grape at the top of his bald head, which itself has the shape of a sphere.  After all the children have had time to giggle, the grape starts

from rest and rolls down without slipping.  It will leave contact with your uncle’s scalp when the radial line joining it to the center of curvature makes what angle with the vertical?

83.(a) A thin rod of length h and mass M is held vertically with its lower end resting on a frictionless horizontal surface. The rod is then released to fall freely. Determine the speed of its center of mass just before it hits the horizontal surface. (b) What If?  Now suppose the rod has a fixed pivot at its lower end. Determine the speed of the rod's center of mass just before it hits the surface.

84.A large, cylindrical roll of tissue paper of initial radius R lies on a long, horizontal surface with the outside end of the paper nailed to the surface. The roll is given a slight shove (vi 0) and commences to unroll. Assume the roll has a uniform density and that mechanical energy is conserved in the process. (a) Determine the speed of the center of mass of the roll when its radius has diminished to r. (b) Calculate a numerical value for this speed at r = 1.00 mm, assuming R = 6.00 m. (c) What If? What happens to the energy of the system when the paper is completely unrolled?

85.A spool of wire of mass M and radius R is unwound under a constant force F (Fig. P10.85). Assuming the spool is a uniform solid cylinder that doesn't slip, show that (a) the acceleration of the center of mass is 4F/3M and (b) the force of friction is to the right and equal in magnitude to F/3. (c) If the cylinder starts from rest and rolls without slipping, what is the speed of its center of mass after it has rolled through a distance d?

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