Q: A vector has components $$x = -6$$ and $$y = 8. $$What is the direction of the vector relative to the positive x-axis?

$$\theta = \tan$$^{-1}$$\left(\frac{8}{-6}\right) = 127^\circ$$

Q: A 2 kg object is suspended by a rope. What is the tension in the rope if the object is at rest? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$T = mg = 2 \times 9.8 = 19.6\ \mathrm{N}$$

Q: A person pushes a 10 kg box with a force of 50 N horizontally. The coefficient of kinetic friction between the box and the floor is 0.3. What is the net force on the box? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$F_{\text{net}} = 50 - (0.3 \times 10 \times 9.8) = 50 - 29.4 = 20.6\ \mathrm{N}$$

Question 1

Which of the following statements best distinguishes a vector from a scalar?

Accepted Answer

A vector has both magnitude and direction, while a scalar has only magnitude.

Question 2

A displacement vector is represented by an arrow 5 units long pointing 37° above the positive x-axis. What are the x- and y-components of this vector?

Accepted Answer

$$x = 5 \cos 37^\circ = 4.0$$, $$y = 5 \sin 37^\circ = 3.0$$

Question 3

Given two vectors, $$\vec{A}$$ and $$\vec{B}$$, with $$\vec{A} = 3\hat{i} + 4\hat{j}$$ and $$\vec{B} = -2\hat{i} + 2\hat{j}$$, what is the magnitude of $$\vec{A} + \vec{B}$$?

Accepted Answer

$$\sqrt{(3 + (-2))^2$ + (4 + 2)^2$} = \sqrt{1^2$ + 6^2$} = \sqrt{37} \approx 6.08$$

Question 4

A ball is thrown horizontally from a 20 m high cliff with an initial speed of 10 m/s. Neglecting air resistance, how far from the base of the cliff does the ball land? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

About 14.3 m

Question 5

Which of the following best describes the acceleration of a projectile at the peak of its trajectory (neglecting air resistance)?

Accepted Answer

It is directed downward with magnitude $$g$$

Question 6

A vector has components $$x = -6$$ and $$y = 8. $$What is the direction of the vector relative to the positive x-axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\frac{8}{-6}ight) = 127^\circ$$

Question 7

A 5 kg box is pulled across a horizontal surface by a rope with a tension of 30 N at an angle of 37° above the horizontal. If the coefficient of kinetic friction is 0.2, what is the acceleration of the box? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

About $$3.2\ \mathrm{m/s^2$}$$

Question 8

Which of the following is a non-contact force?

Accepted Answer

Gravity

Question 9

A car of mass 1000 kg accelerates from rest under a net force of 2000 N. What is its acceleration?

Accepted Answer

$$a = \frac{F}{m} = \frac{2000}{1000} = 2\ \mathrm{m/s^2$}$$

Question 10

A 2 kg object is suspended by a rope. What is the tension in the rope if the object is at rest? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$T = mg = 2 	imes 9.8 = 19.6\ \mathrm{N}$$

Question 11

A block slides down a frictionless incline of 30° with respect to the horizontal. Which of the following correctly gives the acceleration of the block?

Accepted Answer

$$a = g \sin 30^\circ = 4.9\ \mathrm{m/s^2$}$$

Question 12

A person pushes a 10 kg box with a force of 50 N horizontally. The coefficient of kinetic friction between the box and the floor is 0.3. What is the net force on the box? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$F_{	ext{net}} = 50 - (0.3 	imes 10 	imes 9.8) = 50 - 29.4 = 20.6\ \mathrm{N}$$

Question 13

Which of the following best illustrates Newton's Third Law?

Accepted Answer

A swimmer pushes water backward, and the water pushes the swimmer forward.

Question 14

A projectile is launched at an angle of 45° with an initial speed of 20 m/s. What is the maximum height reached by the projectile? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$H = \frac{(20 \sin 45^\$$circ)^2$$}{2 	imes 9.8} \approx 10.2\ \mathrm{m}$$

Question 15

Which of the following is NOT a correct statement about forces?

Accepted Answer

Friction is a non-contact force.

Question 16

A 3 kg object is acted on by two forces: $$\vec{F}_1 = 4\hat{i} + 3\hat{j} N $$and $$\vec{F}_2 = -2\hat{i} + 5\hat{j} N. $$What is the magnitude of the object's acceleration?

Accepted Answer

$$a = \frac{\sqrt{(4 + (-2))^2$ + (3 + 5)^2$}}{3} = \frac{\sqrt{4 + 64}}{3} = \frac{\sqrt{68}}{3} \approx 2.75\ \mathrm{m/s^2$}$$

Question 17

A box is at rest on a horizontal surface. Which of the following statements about the forces acting on the box is correct?

Accepted Answer

The normal force is equal in magnitude and opposite in direction to the weight of the box.

Question 18

A 1.5 kg object is moving in the positive x-direction with a velocity of 4 m/s. A force of 6 N acts in the negative x-direction for 2 seconds. What is the final velocity of the object?

Accepted Answer

$$v_f = v_i + \frac{F}{m} t = 4 + \frac{-6}{1.5} 	imes 2 = 4 - 8 = -4\ \mathrm{m/s}$$

Question 19

A student draws a free-body diagram for a book resting on a table. Which forces should be included?

Accepted Answer

Weight (downward) and normal force (upward)

Vectors, Projectile Motion, and Newton's Laws: Study Notes

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