Page 293 - Dynamics of Mechanical Systems

0593_C08_fm Page 274 Monday, May 6, 2002 2:45 PM

274 Dynamics of Mechanical Systems

P8.7.9: A basketball player wants to shoot a free throw with the minimum possible speed
(thus presumably using the minimum energy and therefore having the greatest control).
If the foul line is 13.75 ft away from the center of the basket (measured horizontally), if
the basket is 10 ft above the floor, and if the player launches the ball 7.5 ft above the floor
as in Figure P8.7.9, what is the optimal angle θ and the minimum speed v?

v

θ
10 ft
7.5 ft

FIGURE P8.7.9 13.75 ft
A basketball free throw.

P8.7.10: During the kickoff in a football game, the ball is kicked end-over-end, rotating 4
revolutions per second. If the ball is kicked 60 yards at a 45° launch angle, determine the
maximum and minimum horizontal components of the velocity of the ends of the ball.
(The ball length is 10 inches.)

Section 8.8 A Rotating Circular Disk
P8.8.1: A thin, circular disk/pulley weighing 35 lb and with radius 15 in. supports (a) a
10-lb force, and (b) a 10-lb weight, as in Figure P8.8.l. In each case, determine the angular
acceleration of the disk and the cable tension.

FIGURE P8.8.1 (a) (b)
A disk supporting (a) a force, and 10 lb
10 lb
(b) a weight.
P8.8.2: A differential pulley has an inner radius of 8 cm and an outer radius of 16 cm.
Cables wrapped around the rim and the inner hub support masses of 5 kg and 3 kg,
respectively, as represented in Figure P8.8.2. Let the pulley be modeled as a thin, circular
disk with mass of 4 kg. If the system is released from rest in the configuration shown,
determine the angular acceleration of the disk and the tensions in each cable.

16 cm
8 cm

3 kg
FIGURE P8.8.2
Differential pulley supporting different masses. 5 kg