Q: A car travels 100 km east in 2 hours, then 60 km west in 1 hour. What is the car's average velocity for the entire trip?

$$\frac{40\ \text{km}}{3\ \text{h}} = 13.3\ \text{km/h}$$ east

Q: A $$0.50 kg $$object moves in a circle of radius $$2.0 m at a $$constant speed of $$4.0 m/s. $$What is the magnitude of the net force acting on the object?

$$0.50 \times (4.0)^2$ / 2.0 = 4.0 N$$

Q: A $$10 kg $$box is pulled up a $$30^\circ$$ incline at constant speed by a rope parallel to the incline. The coefficient of kinetic friction is $$0.20. $$What is the tension in the rope?

$$T = mg \sin 30^\circ + \mu_k mg \cos 30^\circ = 10 \times 9.8 \times 0.5 + 0.2 \times 10 \times 9.8 \times 0.866 = 49 + 16.97 = 65.97 N$$

Q: A $$2.0 kg $$block is attached to a $$3.0 kg $$block by a light string over a frictionless pulley. The $$2.0 kg $$block hangs vertically, and the $$3.0 kg $$block rests on a frictionless table. What is the acceleration of the system?

$$a = \frac{m_2$ g}{m_1$ + m_2$} = \frac{2.0 \times 9.8}{2.0 + 3.0} = 3.92 m/s$^2$$

Q: A $$0.2 kg $$ball is whirled in a horizontal circle of radius $$0.5 m at a $$speed of $$2.0 m/s. $$What is the tension in the string?

$$0.2 \times (2.0)^2$ / 0.5 = 1.6 N$$

Q: A $$1.0 kg $$object is dropped from rest and falls through air. The air resistance force is $$f = kv$$, where $$k = 2.0 kg/s. $$What is the terminal speed of the object?

$$v_t = \frac{mg}{k} = \frac{1.0 \times 9.8}{2.0} = 4.9 m/s$$

Question 1

Which of the following statements best describes a physical theory in physics?

Accepted Answer

A physical theory is an explanation of natural phenomena based on observation and accepted fundamental principles.

Question 2

A car travels 100 km east in 2 hours, then 60 km west in 1 hour. What is the car's average velocity for the entire trip?

Accepted Answer

$$\frac{40\ 	ext{km}}{3\ 	ext{h}} = 13.3\ 	ext{km/h}$$ east

Question 3

A student measures the length of a metal rod as $$12.34 cm $$using a ruler with millimeter markings. Which of the following best represents the uncertainty in this measurement?

Accepted Answer

$$12.34 \pm 0.01 cm$$

Question 4

A vector $$\vec{A}$$ has components $$A_x = 3 m $$and $$A_y = 4 m. $$What is the magnitude and direction of $$\vec{A}$$ relative to the $$x-$$axis?

Accepted Answer

Magnitude $$= 5 m$$, direction $$= 53.1^\circ$$ above the $$x-$$axis

Question 5

A force $$\vec{F} of$$ $$10 N $$acts at an angle of $$30^\circ$$ above the horizontal. What are the $$x$$ and $$y$$ components of $$\vec{F}$$?

Accepted Answer

$$F_x = 10 \cos 30^\circ = 8.66 N$$, $$F_y = 10 \sin 30^\circ = 5.00 N$$

Question 6

A $$2.0 kg $$object is acted on by a net force of $$6.0 N. $$What is its acceleration?

Accepted Answer

$$3.0 m/s$^2$$

Question 7

A $$5.0 kg $$block is at rest on a horizontal surface. The coefficient of static friction between the block and the surface is $$0.40. $$What is the minimum horizontal force required to start moving the block?

Accepted Answer

$$19.6 N$$

Question 8

A $$1.0 kg $$ball is thrown horizontally from a $$20 m $$high cliff with a speed of $$10 m/s. $$Neglecting air resistance, how far from the base of the cliff does the ball land?

Accepted Answer

About $$20 m ($$using $$t = \sqrt{2h/g} = \sqrt{40/9.8} \approx 2.02 s$$, $$x = 10 	imes 2.02 \approx 20 m)$$

Question 9

A $$0.50 kg $$object moves in a circle of radius $$2.0 m at a $$constant speed of $$4.0 m/s. $$What is the magnitude of the net force acting on the object?

Accepted Answer

$$0.50 	imes (4.0)^2$ / 2.0 = 4.0 N$$

Question 10

A $$10 kg $$box is pulled up a $$30^\circ$$ incline at constant speed by a rope parallel to the incline. The coefficient of kinetic friction is $$0.20. $$What is the tension in the rope?

Accepted Answer

$$T = mg \sin 30^\circ + \mu_k mg \cos 30^\circ = 10 	imes 9.8 	imes 0.5 + 0.2 	imes 10 	imes 9.8 	imes 0.866 = 49 + 16.97 = 65.97 N$$

Question 11

A $$2.0 kg $$block is attached to a $$3.0 kg $$block by a light string over a frictionless pulley. The $$2.0 kg $$block hangs vertically, and the $$3.0 kg $$block rests on a frictionless table. What is the acceleration of the system?

Accepted Answer

$$a = \frac{m_2$ g}{m_1$ + m_2$} = \frac{2.0 	imes 9.8}{2.0 + 3.0} = 3.92 m/s$^2$$

Question 12

A $$60 kg $$astronaut weighs $$588 N on $$Earth. What would her weight be on a planet where $$g = 15 m/s$^2$$?

Accepted Answer

$$900 N$$

Question 13

A $$5.0 kg $$object is suspended from a rope and is being lowered at a constant speed. What is the tension in the rope?

Accepted Answer

$$49 N$$

Question 14

A $$2.0 kg $$block is at rest on a horizontal surface. A $$10 N $$horizontal force is applied, but the block does not move. If the coefficient of static friction is $$0.7$$, what is the magnitude of the friction force acting on the block?

Accepted Answer

$$10 N$$

Question 15

A $$0.2 kg $$ball is whirled in a horizontal circle of radius $$0.5 m at a $$speed of $$2.0 m/s. $$What is the tension in the string?

Accepted Answer

$$0.2 	imes (2.0)^2$ / 0.5 = 1.6 N$$

Question 16

A $$1.0 kg $$object is dropped from rest and falls through air. The air resistance force is $$f = kv$$, where $$k = 2.0 kg/s. $$What is the terminal speed of the object?

Accepted Answer

$$v_t = \frac{mg}{k} = \frac{1.0 	imes 9.8}{2.0} = 4.9 m/s$$

Question 17

A $$10 kg $$box is at rest on a rough surface. The coefficient of static friction is $$0.5$$ and the coefficient of kinetic friction is $$0.3. A $$horizontal force of $$40 N is $$applied. What happens?

Accepted Answer

The box does not move; the friction force is $$40 N.$$

Physics with Calculus: Units, Physical Quantities, Vectors, and Motion (Chapters 1–5) – Mini-Textbook Study Notes

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