Book cover for Applied Physics

Applied Physics

Dale Ewen, Neil Schurter, P. Erik Gundersen

ISBN #9780134159386

11th Edition

2,119 Questions

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18,063 Students Helped

Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This section introduces fundamental concepts in describing motion, emphasizing the difference between scalar and vector quantities. It covers how speed, velocity, and acceleration are quantified and applied to real-world problems using vector addition. The chapter explains the importance of considering both magnitude and direction, as seen in examples ranging from automobile speeds to airplane navigation and river crossings.

Learning Objectives

1

Distinguish between scalar speed and vector velocity and understand their roles in describing motion.

2

Utilize vectors to solve problems involving displacement, velocity, and acceleration.

3

Calculate average speed, velocity, and acceleration using the relevant formulas.

4

Analyze two-dimensional motion including projectile motion and the effects of external forces like wind and currents.

5

Apply problem-solving techniques to real-world examples such as vehicle motion and navigation across rivers.

Key Concepts

CONCEPT

DEFINITION

Motion

A change in an object's position relative to a reference point over time.

Speed

A scalar quantity that represents the rate at which an object covers distance. Calculated by dividing distance traveled by time.

Velocity

A vector quantity that not only includes the speed of an object but also the direction of its motion.

Displacement

A vector quantity representing the shortest distance from the initial to the final position of an object along with its direction.

Acceleration

A vector quantity that represents the rate of change of velocity per unit time.

Vector Addition

A method used to combine two or more vectors to determine a resultant vector, taking into account both magnitude and direction.

Example Problems

Example 1

Find the average speed (in the given units) of an auto that travels each distance in the given time. $150 \mathrm{mi}$ in $3.0 \mathrm{~h}($ in $\mathrm{mi} / \mathrm{h})$

Example 2

Find the average speed (in the given units) of an auto that travels each distance in the given time. $190 \mathrm{~m}$ in $8.5 \mathrm{~s}($ in $\mathrm{m} / \mathrm{s})$

Example 3

Find the average speed (in the given units) of an auto that travels each distance in the given time. $8550 \mathrm{~m}$ in $6 \min 35 \mathrm{~s}($ in $\mathrm{m} / \mathrm{s})$

Example 4

Find the average speed (in the given units) of an auto that travels each distance in the given time. $45 \mathrm{~km}$ in $0.50 \mathrm{~h}$ (in $\mathrm{km} / \mathrm{h})$

Example 5

Find the average speed (in the given units) of an auto that travels each distance in the given time. $785 \mathrm{ft}$ in $11.5 \mathrm{~s}$ (in $\mathrm{ft} / \mathrm{s})$
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Step-by-Step Explanations

QUESTION

Find the average speed if an automobile travels 3500 miles in 5.00 hours.

STEP-BY-STEP ANSWER:

Step 1: Identify the total distance and total time. Here, distance = 3500 miles and time = 5.00 hours.
Step 2: Use the formula speed = distance / time.
Step 3: Substitute the values: speed = 3500 mi / 5.00 h.
Step 4: Compute the division to get speed = 700 mi/h.
Final Answer: The average speed is 700 mi/h.

Average Speed

QUESTION

Determine the velocity of a plane that travels 600 km due north in 3.25 hours.

STEP-BY-STEP ANSWER:

Step 1: Write down the displacement (600 km north) and time (3.25 h).
Step 2: Use the equation v_avg = displacement / time with direction noted.
Step 3: Substitute the values: v_avg = 600 km / 3.25 h.
Step 4: Compute the division to obtain approximately 185 km/h, and include the direction 'due north'.
Final Answer: The velocity is 185 km/h due north.

Velocity Calculation

QUESTION

A plane is flying due north at 265 km/h and encounters an eastward wind of 55.0 km/h. Find the new velocity.

STEP-BY-STEP ANSWER:

Step 1: Represent the plane’s velocity as a vector pointing north (y-component = 265 km/h) and the wind as a vector pointing east (x-component = 55.0 km/h).
Step 2: Use the Pythagorean theorem to find the magnitude: R = sqrt((265 km/h)^2 + (55.0 km/h)^2).
Step 3: Calculate R ≈ sqrt(70225 + 3025) = sqrt(73250) ≈ 271 km/h.
Step 4: Determine the direction by calculating the angle with tan(a) = opposite/adjacent = 265/55, then a ≈ 78.3°. Convert to standard position: 180° - 78.3° = 101.7°.
Final Answer: The new velocity of the plane is approximately 271 km/h at 101.7°.

Vector Addition for Resultant Velocity

QUESTION

A dragster accelerates from 0 ft/s to 150 ft/s in 10.0 seconds. Find its acceleration.

STEP-BY-STEP ANSWER:

Step 1: Identify the initial velocity (vi = 0 ft/s) and final velocity (vf = 150 ft/s), and the time interval (t = 10.0 s).
Step 2: Use the acceleration formula: a = (vf - vi) / t.
Step 3: Substitute the values: a = (150 ft/s - 0 ft/s) / 10.0 s.
Step 4: Compute the division: a = 15 ft/s².
Final Answer: The acceleration is 15 ft/s².

Acceleration

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Common Mistakes

  • Failing to include direction when reporting velocity, treating it as a scalar like speed.
  • Confusing distance with displacement, leading to incorrect calculations of velocity.
  • Ignoring the effects of external forces such as wind or current when adding vectors.
  • Mixing up units during calculations, for example, not converting time or distance units appropriately.