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Chapter 11: Problem 4

Which of the following are in static equilibrium? a) a pendulum at the top of its swing b) a merry-go-round spinning at constant angular velocity c) a projectile at the top of its trajectory (with zero velocity) d) all of the above e) none of the above

Short Answer

Expert verified
a) A pendulum at the top of its swing b) A merry-go-round spinning at constant angular velocity c) A projectile at the top of its trajectory (with zero velocity) d) All of the above e) None of the above Answer: e) None of the above

Step by step solution

01

Scenario A: A pendulum at the top of its swing

In this scenario, the pendulum is at the top of its swing, which means that it is momentarily at rest. However, gravity is still acting on the pendulum, causing a downward force. Since there is a net force acting on the pendulum (gravity), it is not in static equilibrium.
02

Scenario B: A merry-go-round spinning at constant angular velocity

In this case, the merry-go-round is spinning at a constant angular velocity, which means there is no net torque acting on it (since it's not accelerating). However, it is not in translational equilibrium since it is constantly moving (rotating). Therefore, this scenario is not in static equilibrium.
03

Scenario C: A projectile at the top of its trajectory (with zero velocity)

At the top of its trajectory, a projectile has zero velocity, which means it is momentarily at rest. However, just like in scenario A, gravity is still acting on the projectile, causing a downward force. This results in a net force acting on the object, and hence, this scenario is also not in static equilibrium.
04

Conclusion

After analyzing all the given scenarios, it's clear that none of them are in static equilibrium. Consequently, the correct answer is option e) none of the above.

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Most popular questions from this chapter

A uniform ladder \(10.0 \mathrm{~m}\) long is leaning against a frictionless wall at an angle of \(60.0^{\circ}\) above the horizontal. The weight of the ladder is \(20.0 \mathrm{lb} . \mathrm{A} 61.0-\mathrm{lb}\) boy climbs \(4.00 \mathrm{~m}\) up the ladder. What is the magnitude of the frictional force exerted on the ladder by the floor?

If the wind is blowing strongly from the east, stable equilibrium for an open umbrella is achieved if its shaft points west. Why is it relatively easy to hold the umbrella directly into the wind (in this case, easterly) but very difficult to hold it perpendicular to the wind?

A \(3.0-\mathrm{kg}\) broom is leaning against a coffee table. \(A\) woman lifts the broom handle with her arm fully stretched so that her hand is a distance of \(0.45 \mathrm{~m}\) from her shoulder What torque is produced on her shoulder if her arm is at an angle of \(50^{\circ}\) below the horizontal? a) \(7.0 \mathrm{~N} \mathrm{~m}\) c) \(8.5 \mathrm{~N} \mathrm{~m}\) b) \(5.8 \mathrm{~N} \mathrm{~m}\) d) \(10.1 \mathrm{~N} \mathrm{~m}\)

The angular displacement of a torsional spring is proportional to the applied torque; that is \(\tau=\kappa \theta,\) where \(\kappa\) is a constant. Suppose that such a spring is mounted to an arm that moves in a vertical plane. The mass of the arm is \(45.0 \mathrm{~g}\), and it is \(12.0 \mathrm{~cm}\) long. The arm-spring system is at equilibrium with the arm at an angular displacement of \(17.0^{\circ}\) with respect to the horizontal. If a mass of \(0.420 \mathrm{~kg}\) is hung from the arm \(9.00 \mathrm{~cm}\) from the axle, what will be the angular displacement in the new equilibrium position (relative to that with the unloaded spring)?

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