Q: A vector $$ \vec{A} $$ has a magnitude of 10 units and makes an angle of 30° with the x-axis. What are the x- and y-components of $$ \vec{A} $$?

$$A_x = 10 \times \cos(30^\circ) = 8.66$$, $$A_y = 10 \times \sin(30^\circ) = 5.0$$

Q: A ball weighing 50 N is held in equilibrium by two ropes. One rope makes a 20° angle with the vertical. What is the vertical component of the tension in this rope?

$$T_{1y} = T_1$ \times \cos(20^\circ)$$

Q: A vector $$ \vec{B} $$ has components $$B_x = -2$$, $$B_y = 2. $$What is the magnitude and direction (angle from the x-axis) of $$ \vec{B} $$?

$$|\vec{B}| = \sqrt{(-2)^2$ + 2^2$} = 2.83$$, \theta = \$$tan^{-1}(2 / -2) = 135$$^\circ$

Q: A 400 g mass is suspended by two strings. One string pulls horizontally with 3 N, and the other pulls vertically. What is the tension in the vertical string?

$$T_{vertical} = w = 400 \text{ g} \times 9.8 \text{ m/s}^2 = 3.92 \text{ N}$$

Q: If a vector $$ \vec{A} $$ has components $$A_x = 3$$, $$A_y = -2$$, what is the angle $$ \theta it $$makes with the x-axis?

$$\theta = \tan$$^{-1}$$(-2 / 3) = -33.7^\circ$$

Q: A spring scale is used to pull a mass horizontally with a force of 3 N while the mass hangs vertically with a weight of 4 N. What is the total tension in the string?

$$T = \sqrt{3^2$ + 4^2$} = 5 \text{ N}$$

Q: A vector $$ \vec{A} $$ has a magnitude of 8 units and points at an angle of 60° above the x-axis. What is its y-component?

$$A_y = 8 \times \sin(60^\circ) = 6.93$$

Question 1

A vector $$ \vec{A} $$ has a magnitude of 10 units and makes an angle of 30° with the x-axis. What are the x- and y-components of $$ \vec{A} $$?

Accepted Answer

$$A_x = 10 	imes \cos(30^\circ) = 8.66$$, $$A_y = 10 	imes \sin(30^\circ) = 5.0$$

Question 2

If $$ \vec{D} $$ points along the x-axis and $$ \vec{E} $$ points along the y-axis, what is the magnitude of $$ \vec{F} = \vec{D} + \vec{E}  if$$ $$ |\vec{D}| = 3 $$ units and $$ |\vec{E}| = 4 $$ units?

Accepted Answer

$$|\vec{F}| = \sqrt{3^2$ + 4^2$} = 5$$

Question 3

A ball weighing 50 N is held in equilibrium by two ropes. One rope makes a 20° angle with the vertical. What is the vertical component of the tension in this rope?

Accepted Answer

$$T_{1y} = T_1$ 	imes \cos(20^\circ)$$

Question 4

Which equation must be satisfied for an object to be in static equilibrium?

Accepted Answer

$$\sum F_x = 0$$ and $$\sum F_y = 0$$

Question 5

A vector $$ \vec{B} $$ has components $$B_x = -2$$, $$B_y = 2. $$What is the magnitude and direction (angle from the x-axis) of $$ \vec{B} $$?

Accepted Answer

$$|\vec{B}| = \sqrt{(-2)^2$ + 2^2$} = 2.83$$, 	heta = \$$tan^{-1}(2 / -2) = 135$$^\circ$

Question 6

A 400 g mass is suspended by two strings. One string pulls horizontally with 3 N, and the other pulls vertically. What is the tension in the vertical string?

Accepted Answer

$$T_{vertical} = w = 400 	ext{ g} 	imes 9.8 	ext{ m/s}^2 = 3.92 	ext{ N}$$

Question 7

If a vector $$ \vec{A} $$ has components $$A_x = 3$$, $$A_y = -2$$, what is the angle $$ 	heta  it $$makes with the x-axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$(-2 / 3) = -33.7^\circ$$

Question 8

A spring scale is used to pull a mass horizontally with a force of 3 N while the mass hangs vertically with a weight of 4 N. What is the total tension in the string?

Accepted Answer

$$T = \sqrt{3^2$ + 4^2$} = 5 	ext{ N}$$

Question 9

Which of the following best describes the tip-to-tail rule for vector addition?

Accepted Answer

Slide the tail of the second vector to the tip of the first vector and draw the resultant from the tail of the first to the tip of the second.

Question 10

A vector $$ \vec{A} $$ has a magnitude of 8 units and points at an angle of 60° above the x-axis. What is its y-component?

Accepted Answer

$$A_y = 8 	imes \sin(60^\circ) = 6.93$$

Question 11

A mass is held in static equilibrium by two ropes. Rope 1 pulls at an angle $$ 	heta $$ above the horizontal, and Rope 2 pulls horizontally. If the weight of the mass is $$ w $$, what must the vertical component of Rope 1's tension equal?

Accepted Answer

$$T_1$$ \sin 	heta = w$$

Question 12

If a vector $$ \vec{C} $$ has components $$C_x = 0$$, $$C_y = -6$$, what is its magnitude and direction?

Accepted Answer

$$|\vec{C}| = 6$$, 	heta = -90^\circ$

Question 13

A 50 N ball is pulled back by a rope at 20° from vertical. If the horizontal tension in the second rope is 18 N, what is the total tension in the angled rope?

Accepted Answer

$$T_1$$ = \sqrt{$$50^2$$ + $$18^2$$} = 53.1 	ext{ N}$$

Question 14

Which trigonometric function relates the opposite side to the hypotenuse in a right triangle?

Accepted Answer

$$\sin 	heta = \frac{O}{H}$$

Question 15

A vector $$ \vec{A} $$ has components $$A_x = 10$$, $$A_y = -4. $$What is its magnitude?

Accepted Answer

$$|\vec{A}| = \sqrt{10^2$ + (-4)^2$} = 10.77$$

Question 16

If the sum of the forces in the x-direction is not zero, what can be said about the object's motion?

Accepted Answer

The object will accelerate in the x-direction.

Question 17

A mass is suspended by two ropes, one red and one green. If the tension in the red rope is 10 N and the green rope is 8.66 N, what is the mass of the ball?

Accepted Answer

$$m = \frac{\sqrt{10^2$ + 8.66^2$}}{9.8} = 1.36 	ext{ kg}$$

EXAM #3 DAY 14: Vectors and Static Equilibrium: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards