Q: Which of the following correctly states the two conditions required for an object to be in static equilibrium?

$$\sum \vec{F} = 0$$ and $$\sum \vec{\tau} = 0$$

Q: A ladder leans against a frictionless wall, making an angle $$\theta$$ with the ground. If a person climbs one-third of the way up, which equation would you use to find the minimum coefficient of static friction at the base?

$$\sum \tau = 0$$ about the base

Question 1

Which of the following correctly states the two conditions required for an object to be in static equilibrium?

Accepted Answer

$$\sum \vec{F} = 0$$ and $$\sum \vec{	au} = 0$$

Question 2

A uniform plank of length $$L = 6.0\ \mathrm{m}$$ and mass $$M = 90\ \mathrm{kg}$$ rests on sawhorses separated by $$D = 1.5\ \mathrm{m}$$ and equidistant from the center. If a person stands at the right end, what is the maximum mass the person can have for the plank to remain at rest?

Accepted Answer

$$m = 270\ \mathrm{kg}$$

Question 3

The center of gravity of an object is defined as:

Accepted Answer

The point where the entire weight of the object can be considered to act.

Question 4

A car is parked on an incline. Under what condition will the car tip over rather than slide down the incline?

Accepted Answer

When the center of gravity is outside the area of support.

Question 5

A ladder leans against a frictionless wall, making an angle $$	heta$$ with the ground. If a person climbs one-third of the way up, which equation would you use to find the minimum coefficient of static friction at the base?

Accepted Answer

$$\sum 	au = 0$$ about the base

Question 6

A diver weighing $$500\ \mathrm{N}$$ stands at the end of a $$3.00\ \mathrm{m}$$ diving board supported $$1.00\ \mathrm{m}$$ from the end. The board weighs $$280\ \mathrm{N}. $$What is the force at the support point?

Accepted Answer

$$640\ \mathrm{N}$$ upward

Question 7

When an object is suspended from a single point and is in equilibrium, where is its center of gravity located?

Accepted Answer

Directly above or below the point of suspension.

Question 8

A boom weighing $$2600\ \mathrm{N} is $$attached to a frictionless pivot at its lower end. Its center of gravity is $$35\% of $$its length from the pivot. What is the first step in solving for the tension in the guy wire?

Accepted Answer

Draw a free-body diagram of the boom.

Question 9

In the plank exercise, an athlete supports $$66.0\% of $$his weight on his forearms and $$34.0\% on $$his toes. If the distance from his toes to his forearms is $$1.53\ \mathrm{m}$$, how far from his toes is his center of gravity?

Accepted Answer

$$1.01\ \mathrm{m}$$

Question 10

Which of the following is true for an object in static equilibrium?

Accepted Answer

The sum of all external forces and the sum of all external torques are zero.

Question 11

A uniform horizontal beam is supported at both ends. If a heavy object is placed closer to one end, what happens to the forces at the supports?

Accepted Answer

The support closer to the object exerts a greater upward force.

Question 12

A dumbbell is held in equilibrium by the forearm. Which forces must be considered in the torque equation about the elbow?

Accepted Answer

The weight of the dumbbell, the tension in the tendon, and the force from the upper arm.

Question 13

If the net external force on an object is zero but the net external torque is not zero, what will happen?

Accepted Answer

The object will rotate but not translate.

Question 14

Which of the following best describes the effect of raising the center of gravity of a vehicle?

Accepted Answer

It makes the vehicle more likely to tip over on an incline.

Question 15

A non-uniform beam is supported at one end and held by a guy wire at the other. The center of gravity is not at the midpoint. To solve for the tension in the wire, which principle is most useful?

Accepted Answer

The sum of torques about the pivot must be zero.

Question 16

Which of the following is NOT a correct step in the problem-solving strategy for static equilibrium?

Accepted Answer

Ignore the direction of forces when summing torques.

Chapter 11: Equilibrium and Elasticity – Structured Study Notes

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