Q: A body of mass $8\ \mathrm{kg}$ is placed on a smooth inclined plane at $30^\circ$ to the horizontal. What is the component of the weight acting down the plane?

$8 \times 9.8 \times \sin 30^\circ$

Q: A body of mass $4\ \mathrm{kg}$ is placed on a smooth inclined plane at $30^\circ$ to the horizontal. A force $F$ acts up the plane and the body moves with uniform velocity. What is the value of $F$?

$4 \times 9.8 \times \sin 30^\circ$

Q: A force $\vec{F} = 2\vec{i} + 3\vec{j} + 4\vec{k}$ acts at point $A(1,2,3)$. What is the general formula for the moment of $\vec{F}$ about the origin?

$\vec{M}_O = \vec{r}_A \times \vec{F}$

Q: If a force $\vec{F}$ acts at point $A(x_1, y_1)$, and you want to find its moment about point $O(0,0)$, which formula should you use?

$\vec{M}_O = \vec{r}_A \times \vec{F}$

Question 1

A force $\vec{F} = 3\vec{i} + 4\vec{j}$ acts at point $A(3,0)$. What is the moment vector of $\vec{F}$ with respect to the point $B(-2,4)$?

Accepted Answer

$\vec{M}_B = 18\vec{k}$

Question 2

If a force $\vec{F}$ acts at a point such that its line of action passes through the origin, what is the moment of $\vec{F}$ about the origin?

Accepted Answer

It is the zero vector

Question 3

Two forces $\vec{F}_1 = 2\vec{i} + 3\vec{j}$ and $\vec{F}_2 = -\vec{i} + 4\vec{j}$ act at points $A(2,5)$ and $B(1,4)$ respectively. What is the sum of the moments of these forces about the origin?

Accepted Answer

$-16\vec{k}$

Question 4

A uniform rod of length $60\ \mathrm{cm}$ and weight $40\ \mathrm{gm\ wt}$ rests on a support $20\ \mathrm{cm}$ from end $A$. If the rod is kept in equilibrium horizontally by a light vertical string at end $B$, what is the tension in the string?

Accepted Answer

$10\ \mathrm{gm\ wt}$

Question 5

A couple consists of two forces of equal magnitude $F$ acting in opposite directions along parallel lines separated by a distance $d$. What is the moment of the couple?

Accepted Answer

$Fd$

Question 6

A force $\vec{F} = 2\vec{i} + 3\vec{j}$ acts at point $A(3,2)$. What is the moment of $\vec{F}$ about point $B(2,2,-1)$ in 3D?

Accepted Answer

$\vec{M}_B = 7\vec{k}$

Question 7

If the sum of the algebraic measures of a set of coplanar parallel forces is zero, and the sum of their moments about any point is also zero, what can be concluded about the system?

Accepted Answer

The system is in equilibrium

Question 8

A body of mass $8\ \mathrm{kg}$ is placed on a smooth inclined plane at $30^\circ$ to the horizontal. What is the component of the weight acting down the plane?

Accepted Answer

$8 	imes 9.8 	imes \sin 30^\circ$

Question 9

A force $\vec{F} = m\vec{i} + n\vec{j}$ acts at point $A(4,2)$. If its moment about the origin is $-15\vec{k}$ and its moment about $B(0,5)$ is $15\vec{k}$, what are the values of $m$ and $n$?

Accepted Answer

$m = 3, n = 6$

Question 10

A uniform rod of length $90\ \mathrm{cm}$ and weight $30\ \mathrm{N}$ rests horizontally on two supports, one at $A$ and the other at $C$ which is $30\ \mathrm{cm}$ from $B$. If a weight of $20\ \mathrm{N}$ is suspended at a point $15\ \mathrm{cm}$ from $B$, what is the pressure on support $A$?

Accepted Answer

$25\ \mathrm{N}$

Question 11

If two parallel forces of $7\ \mathrm{N}$ and $12\ \mathrm{N}$ act in opposite directions at points $A$ and $B$ separated by $20\ \mathrm{cm}$, what is the magnitude of the resultant force?

Accepted Answer

$5\ \mathrm{N}$

Question 12

A body of mass $4\ \mathrm{kg}$ is placed on a smooth inclined plane at $30^\circ$ to the horizontal. A force $F$ acts up the plane and the body moves with uniform velocity. What is the value of $F$?

Accepted Answer

$4 	imes 9.8 	imes \sin 30^\circ$

Question 13

A couple consists of two forces each of magnitude $70\ \mathrm{N}$ and the moment of the couple is $350\ \mathrm{N\cdot m}$. What is the perpendicular distance between the lines of action of the forces?

Accepted Answer

$2.5\ \mathrm{m}$

Question 14

A force $\vec{F} = 2\vec{i} + 3\vec{j} + 4\vec{k}$ acts at point $A(1,2,3)$. What is the general formula for the moment of $\vec{F}$ about the origin?

Accepted Answer

$\vec{M}_O = \vec{r}_A 	imes \vec{F}$

Question 15

A system of coplanar forces is equivalent to a couple if:

Accepted Answer

The sum of the forces is zero and the sum of the moments is nonzero

Question 16

If a force $\vec{F}$ acts at point $A(x_1, y_1)$, and you want to find its moment about point $O(0,0)$, which formula should you use?

Accepted Answer

$\vec{M}_O = \vec{r}_A 	imes \vec{F}$

Question 17

A uniform rod of length $2\ \mathrm{m}$ and mass $75\ \mathrm{kg}$ rests horizontally on two supports at its ends. A weight of $15\ \mathrm{kg}$ is suspended from a point $50\ \mathrm{cm}$ from one end. What is the reaction at the support closer to the hanging weight?

Accepted Answer

$40\ \mathrm{kg}$

Question 18

If the sum of the moments of several parallel forces about a point equals zero, what does this imply about the resultant?

Accepted Answer

The resultant passes through the same point

Question 19

A force $\vec{F} = 6\vec{i} + 8\vec{j}$ acts at point $A(-1,2)$. What is the moment vector of $\vec{F}$ with respect to point $B(2,5)$?

Accepted Answer

$\vec{M}_B = 30\vec{k}$

Statics and Mechanics: Moments, Forces, and Couples (Mini-Textbook Study Notes)

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