Page 370 - Dynamics of Mechanical Systems

0593_C10_fm Page 351 Monday, May 6, 2002 2:57 PM

Introduction to Energy Methods 351

P10.6.22: A 300-lb flywheel with radius of gyration of 15 in. is rotating at 3000 rpm. A
bearing failure causes a small friction moment of 2 ft⋅lb which in turn causes the flywheel
to slow and eventually stop. How many turns does the flywheel make before coming to
a stop?

Section 10.10 Motor Vehicle Accident Reconstruction
P10.10.1: All four wheels of a car leave 75-ft-long skid marks in coming to a stop on a
level roadway. If the coefficient of friction between the tires and the road surface is 0.75,
determine the speed of the car at the beginning of the skid marks.
P10.10.2: The front wheels of a car leave 70 ft of skid marks and its rear wheels leave 50
ft of skid marks in coming to a stop on a level roadway. If the coefficient of friction between
the tires and the roadway is 0.80, and if 60% of the vehicle weight is on the front wheels,
determine the speed of the car at the beginning of the skid marks.
P10.10.3: A car slides to a stop leaving skid marks of length s (measured in feet) on a level
roadway. If the coefficient of friction between the tires and the roadway is µ, show that
the speed v (in miles per hour) of the car at the beginning of the skid marks is given by
the simple expression:

v = 30µ s

P10.10.4: See Problem P10.10.3. Suppose that the roadway, instead of being level, has a
slight down slope in the direction of travel as represented in Figure P10.10.4. If the down
slope angle is θ (measured in radians) as shown, show that the speed formula of Problem
P10.10.3 should be modified to:

−
v = 30 (µθ s )

v
FIGURE P10.10.4 θ A
An automobile A skidding to a stop on
a downslope.

P10.10.5: An automobile leaves 50 ft of skid marks before striking a pole at 20 mph. Find
the speed of the vehicle at the beginning of the skid marks if the roadway is level and if
the coefficient of friction between the tires and the roadway is 0.65. Assume the vehicle
stops upon hitting the pole.
P10.10.6: A pickup truck leaves 30 ft of skid marks before colliding with the rear of a
stopped automobile. Following the collision, the two vehicles slide together (a plastic
collision) for 25 ft. Let the coefficient of friction between the pickup truck tires and the
roadway be 0.7; after the collision, for the sliding vehicles together, let the coefficient of
friction with the roadway be 0.5. Let the weights of the pickup truck and automobile be
3500 lb and 2800 lb, respectively. Find the speed of the pickup truck at the beginning of
the skid marks.
P10.10.7: Repeat Problem P10.10.6 if just before collision, instead of being stopped, the
automobile is moving at 10 mph in the same direction as the pickup truck.