Q: For a rigid body to be in equilibrium, which set of equations must be satisfied?

$$\sum F = 0$$ and $$\sum \tau = 0$$

Question 1

Which of the following statements best distinguishes mass from weight?

Accepted Answer

Mass is the quantity of matter and does not vary by location, while weight is the force due to gravity and varies with location.

Question 2

The position vector for the center of mass $$\vec{r}_{cm} of a $$system of particles is given by which equation?

Accepted Answer

$$\vec{r}_{cm} = \frac{\sum m_i \vec{r}_i}{\sum m_i}$$

Question 3

A 10 kg object is taken from Earth to the Moon. Which of the following is true?

Accepted Answer

Its mass remains the same, but its weight decreases.

Question 4

Which of the following is a valid assumption when modeling a rigid body in equilibrium?

Accepted Answer

The gravitational field $$g is $$constant.

Question 5

For a rigid body to be in equilibrium, which set of equations must be satisfied?

Accepted Answer

$$\sum F = 0$$ and $$\sum 	au = 0$$

Question 6

A ladder leans against a wall making an angle $$	heta$$ with the ground. Which of the following would increase the ladder's stability?

Accepted Answer

Lowering the center of gravity and increasing the area of support.

Question 7

The center of gravity $$\vec{r}_{cg}$$ for a collection of particles is given by:

Accepted Answer

$$\vec{r}_{cg} = \frac{\sum m_i g \vec{r}_i}{\sum m_i g}$$

Question 8

Why is it important to select and stick with a single origin when calculating torques in a rigid body problem?

Accepted Answer

Because torque values depend on the chosen origin and switching origins can lead to inconsistent results.

Question 9

A uniform beam is supported at both ends and a heavy object is placed at its center. What happens to the stability if the object is moved closer to one end?

Accepted Answer

The stability decreases because the center of gravity moves closer to the edge of the support area.

Question 10

Which of the following is NOT a limitation of equilibrium analysis for rigid bodies?

Accepted Answer

It always provides a unique solution even with fewer equations than unknowns.

Question 11

A 5 m ladder of weight 180 N leans against a wall at $$53.1^\circ$$ with a person of weight 800 N standing one third up the ladder. Which equation would you use to find the normal force at the base?

Accepted Answer

$$\sum F_y = 0$$

Question 12

Which of the following best describes a rigid body?

Accepted Answer

A body that does not deform and in which all forces between particles are balanced.

Question 13

In a free-body diagram, why must all forces be brought together at the center of gravity?

Accepted Answer

Because it simplifies the calculation of net force and torque.

Question 14

Which of the following is a correct method for finding the center of gravity of a complex object?

Accepted Answer

Divide the object into geometric shapes, find the center of gravity of each, and treat them as particles.

Question 15

If a force is applied to a rigid body at a point not passing through the center of mass, what is the resulting motion?

Accepted Answer

The center of mass moves like a particle and the body may experience torque.

Question 16

Which of the following is a real-world example where the assumption of a rigid body fails?

Accepted Answer

A gymnast bending a flexible bar during a routine.

Question 17

Why is the assumption 'material is homogeneous' useful in center of gravity calculations?

Accepted Answer

It allows the use of geometric rules to find the center of gravity.

Question 18

Which of the following best describes the effect of lowering the center of gravity on an object's stability?

Accepted Answer

It increases stability.

Centre of Gravity and Rigid-Body Equilibrium: Study Notes for PHY1020

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