When bicycle and motorcycle riders “pop a wheelie,” a large acceleration causes the bike’s front wheel to leave the ground. Let M be the total mass of the bike-plus-rider system: let x and y be the horizontal and vertical distance of this system’s CM from the rear wheel’s point of contact with the ground (Fig. 10–72). ( a ) Determine the horizontal acceleration a required to barely lift the hike’s front wheel off of the ground, ( b ) To minimize the acceleration necessary to pop a wheelie, should x be made as small or as large as possible? How about y ? How should a rider position his or her body on the bike in order to achieve these optimal values for x and y? ( c ) If x = 35 cm and y = 95 cm, find a .
When bicycle and motorcycle riders “pop a wheelie,” a large acceleration causes the bike’s front wheel to leave the ground. Let M be the total mass of the bike-plus-rider system: let x and y be the horizontal and vertical distance of this system’s CM from the rear wheel’s point of contact with the ground (Fig. 10–72). ( a ) Determine the horizontal acceleration a required to barely lift the hike’s front wheel off of the ground, ( b ) To minimize the acceleration necessary to pop a wheelie, should x be made as small or as large as possible? How about y ? How should a rider position his or her body on the bike in order to achieve these optimal values for x and y? ( c ) If x = 35 cm and y = 95 cm, find a .
When bicycle and motorcycle riders “pop a wheelie,” a large acceleration causes the bike’s front wheel to leave the ground. Let M be the total mass of the bike-plus-rider system: let x and y be the horizontal and vertical distance of this system’s CM from the rear wheel’s point of contact with the ground (Fig. 10–72). (a) Determine the horizontal acceleration a required to barely lift the hike’s front wheel off of the ground, (b) To minimize the acceleration necessary to pop a wheelie, should x be made as small or as large as possible? How about y? How should a rider position his or her body on the bike in order to achieve these optimal values for x and y? (c) If x = 35 cm and y = 95 cm, find a.
(III) An Atwood machine consists of two masses,
ma = 65 kg and mg = 75 kg, connected by a massless
inelastic cord that passes over a pulley free to rotate,
Fig. 8–52. The pulley is a solid cylin-
der of radius R = 0.45 m and mass
6.0 kg. (a) Determine the accelera-
tion of each mass. (b) What % error
would be made if the moment of
ROR
inertia of the pulley is ignored?
[Hint: The tensions FTA and FrB are
not equal. We discussed the Atwood
machine in Example 4–13, assuming
I = 0 for the pulley.]
FTA
TB
FIGURE 8–52 Problem 47.
MB
Atwood machine.
A 4.00-kg mass and a 3.00-kg mass are attached to opposite ends of a very light 42.0-cm-long horizontal rod (Fig. 8–61). The system is rotating at angular speed v = 5.60 rad/s about a vertical axle at the center of the rod. Determine (a) the kinetic energy KE of the system, and (b) the net force on each mass.
A 4.00-kg mass and a 3.00-kg mass are attached to opposite
ends of a very light 42.0-cm-long horizontal rod (Fig. 8–61).
The system is rotating at angular speed w = 5.60 rad/s
about a vertical axle at the center of the rod. Determine
(a) the kinetic energy KE of the system, and (b) the net
force on each mass.
3.00 kg
4.00 kg
FIGURE 8-61 Problem 87.
Chapter 10 Solutions
Physics for Science and Engineering With Modern Physics, VI - Student Study Guide
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