15. Rotational Equilibrium

In a hexagonal unit cell, which of the following sets of indices correctly represents the direction from the origin to the point with coordinates $1,1,0$ in the four-index Miller-Bravais notation?

A system consists of two blocks of masses $m_1$ and $m_2$ connected by a light string over a frictionless pulley. If the system is in equilibrium, which of the following must be true about the relationship between $m_1$ and $m_2$?

A uniform stationary ladder of length $l$ leans against a smooth vertical wall, making an angle $\theta$ with the ground. If the coefficient of static friction between the ladder and the ground is $\mu$, which of the following expressions gives the minimum value of $\mu$ required to prevent the ladder from slipping?

Which of the following conditions must be satisfied for a system to be in rotational equilibrium?

A uniform beam of length $L$ and mass $M$ rests horizontally on two supports, one at the left end and one a distance $d$ from the right end. If a person of mass $m$ walks toward the right end, how close can the person get to the right end of the beam before the beam begins to tip over the right support?

In the context of equilibrium with multiple objects, what does it mean for a system to be in a state of rotational equilibrium?

A 20 kg, 5 m-long bar of uniform mass distribution is attached to the ceiling by a light string, as shown. Because the string is off-center (2 m from the right edge), the bar does not hang horizontally. To fix this, you place a small object on the right edge of the bar. What mass should this object have, to cause the bar to balance horizontally?

Two kids (m,_LEFT = 50 kg, m,_RIGHT = 40 kg) sit on the very ends of a 5 m-long, 30 kg seesaw. How far from the left end of the seesaw should the fulcrum be placed so the system is at equilibrium? (Remember the weight of the seesaw!)

Two people are carrying a uniform wooden board that is 3.00 m long and weighs 160 N. If one person applies an upward force equal to 60 N at one end, at what point does the other person lift? Begin with a free-body diagram of the board.

Two people carry a heavy electric motor by placing it on a light board 2.00 m long. One person lifts at one end with a force of 400 N, and the other lifts the opposite end with a force of 600 N. What is the weight of the motor, and where along the board is its center of gravity located?

A 0.120-kg, 50.0-cm-long uniform bar has a small 0.055-kg mass glued to its left end and a small 0.110-kg mass glued to the other end. The two small masses can each be treated as point masses. You want to balance this system horizontally on a fulcrum placed just under its center of gravity. How far from the left end should the fulcrum be placed?

The mobile in Fig. 12–91 is in equilibrium. Object B has mass of 0.748 kg. Determine the masses of objects A, C, and D. (Neglect the weights of the crossbars.)

In Fig. 12–103, consider the right-hand (northernmost) section of the Golden Gate Bridge, which has a length d₁ = 343 m. Assume the cg of this span is halfway between the tower and anchor. Determine F_T1 and F_T2 (which act on the northernmost cable) in terms of mg, the weight of the northernmost span, and calculate the tower height h needed for equilibrium. Assume the roadway is supported only by the suspension cables, and neglect the mass of the cables and vertical wires. [Hint: F_T3 does not act on this section.]