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.
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.
(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.
Chapter 10 Solutions
Physics for Scientists and Engineers with Modern Physics
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