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Assignment 5-9
Newport AP Physics—C. Appel
Chapter 8 Problems
59.
Review Problem. Suppose the incline is frictionless for the system
described in Problem 58 (see Fig. P8.58). The block is released from rest
with the spring initially unstretched. (a) How far does it move down the
incline before coming to rest? (b) What is its acceleration at its lowest
point? Is the acceleration constant? (c) Describe the energy
transformations that occur during the descent.
68.
(“Doc” Problem) A ball is tied to one end of a string. The other end of the
string is fixed. The ball is set in motion around a vertical circle without
friction. At the top of the circle, the ball has a speed of vi  Rg , as
shown in Figure P8.68. At what angle θ should the string be cut so that the
ball will travel through the center of the circle?
70.
A pendulum comprising a string of length L and a sphere swings in the
vertical plane. The string hits a peg located a distance d below the point of suspension (Fig. P8.70). (a)
Show that if the sphere is released from a height below that of the peg, it will
return to this height after striking the peg. (b) Show that if the pendulum is
released from the horizontal position (θ = 90°) and is to swing in a complete
circle centered on the peg, then the minimum value of d must be 3L/5.
Chapter 11 Problems
9.
13.


Given M  6iˆ  2 ˆj  kˆ and N  2iˆ  ˆj  3kˆ , calculate the vector product
 
M N.

A force of F  2.00iˆ  3.00 ˆj N is applied to an object that is pivoted about a fixed axis aligned along
the z coordinate axis. If the force is applied at the point

r  4.00iˆ  5.00 ˆj  0kˆ m, find (a) the magnitude of the net torque about
the z axis and (b) the direction of the torque vector τ.


19.
A light, rigid rod 1.00 m in length joins two particles—with masses 4.00
kg and 3.00 kg—at its ends. The combination rotates in the xy plane about
a pivot through the center of the rod (Fig. P11.19). Determine the angular
momentum of the system about the origin when the speed of each particle
is 5.00 m/s.
21.
The position vector of a particle of mass 2.00 kg is given as a function of

time by r  6.00iˆ  5.00tj m. Determine the angular momentum of the
particle about the origin as a function of time.
26.
Heading straight toward the summit of Pike’s Peak, an airplane of mass 12,000 kg flies over the plains
of Kansas at a nearly constant altitude of 4.30 km and with a constant velocity of 175 m/s westward. (a)
What is the airplane’s vector angular momentum relative to a wheat farmer on the ground directly below
the airplane? (b) Does this value change as the airplane continues its motion along a straight line? (c)
What is its angular momentum relative to the summit of Pike’s Peak?


Answers:
8-59: (a) 0.236 m (b) 5.90 m/s2, not constant
8-68: “Doc” Problem
8-70: Proof
11-9:  7iˆ  16 ˆj   10kˆ
11-13: (a) 2.00 N∙m (b) kˆ
11-19: 17.5 kgμm/s2 in the +z direction
11-21: 60.0kˆ kg∙m2/s
11-26: (a) 9.03 x 109 kg∙m2/s (south) (b) No (c) Zero