Physics 2010 Practice Exam 1 – Step-by-Step Study Guidance

Q1. Evaluate the expression $3.125 \times 0.03974 + 21.1$, ensuring that your answer is correct to the right number of significant figures.

Background

Topic: Significant Figures and Order of Operations

This question tests your ability to perform calculations with the correct number of significant figures, following the rules for multiplication and addition.

Key Terms and Formulas:

• Significant Figures: The digits in a number that carry meaning contributing to its precision.

• Order of Operations: Perform multiplication before addition.

• Rules:

  • For multiplication/division: The result should have as many significant figures as the factor with the fewest significant figures.

  • For addition/subtraction: The result should have as many decimal places as the number with the fewest decimal places.

Step-by-Step Guidance

1. First, multiply $3.125$ by $0.03974$. Count the significant figures in each factor: $3.125$ (4 sig figs), $0.03974$ (4 sig figs).

2. Calculate the product and keep 4 significant figures in your intermediate result.

3. Add the result to $21.1$. Note that $21.1$ has 1 decimal place, so your final answer should be rounded to 1 decimal place.

4. Be careful to apply the correct rounding rules at each step.

Try solving on your own before revealing the answer!

Q2. The metric system is preferred over the British (Imperial) system for the following main reason:

Background

Topic: Measurement Systems

This question tests your understanding of why the metric system is widely used in science and engineering.

Key Terms:

• Metric System: A decimal-based system of measurement.

• British (Imperial) System: A system of measurement using units like feet, pounds, and gallons.

Step-by-Step Guidance

1. Read each answer choice carefully and consider what makes the metric system easier to use, especially for conversions.

2. Recall that the metric system is based on powers of ten, making calculations and conversions straightforward.

3. Eliminate choices that are not directly related to the ease of conversion or calculation.

Try solving on your own before revealing the answer!

Q3. A reasonable estimate for a typical male college student is:

Background

Topic: Estimation and Orders of Magnitude

This question tests your ability to make reasonable estimates for physical quantities, specifically mass.

Key Terms:

• Order of Magnitude: The scale or size of a value in powers of ten.

• Typical Mass: The average mass for an adult male.

Step-by-Step Guidance

1. Recall that 1 kg is about 2.2 pounds. Think about the average weight of a college-aged male in pounds and convert to kilograms if needed.

2. Compare the given options to your estimate and eliminate values that are clearly too low or too high.

Try solving on your own before revealing the answer!

Q4. There is a rectangular field in the quad of a college campus with a length of 95.7 m and a width of 108.6 m. What is the area of the rectangle?

Background

Topic: Area Calculation and Significant Figures

This question tests your ability to calculate the area of a rectangle and report the answer with the correct number of significant figures.

Key Formula:

$A = l \times w$

• $A$ = area

• $l$ = length

• $w$ = width

Step-by-Step Guidance

1. Write down the formula for the area of a rectangle: $A = l \times w$.

2. Plug in the given values: $l = 95.7$ m, $w = 108.6$ m.

3. Multiply the two values, keeping track of significant figures (both have 3 significant figures).

4. Round your answer to the correct number of significant figures.

Try solving on your own before revealing the answer!

Q5. The mass of a particular type of bacterium is about $1.23 \times 10^{-13}$ kg. A petri dish contains nearly $2.75 \times 10^{9}$ of them. What is the combined mass of all the bacteria?

Background

Topic: Scientific Notation and Multiplication

This question tests your ability to multiply numbers in scientific notation and apply significant figures.

Key Formula:

$\text{Total mass} = \text{mass per bacterium} \times \text{number of bacteria}$

Step-by-Step Guidance

1. Write the formula: $\text{Total mass} = (1.23 \times 10^{-13}) \times (2.75 \times 10^{9})$.

2. Multiply the coefficients: $1.23 \times 2.75$.

3. Add the exponents: $10^{-13} \times 10^{9} = 10^{-4}$.

4. Combine your results and round to the correct number of significant figures.

Try solving on your own before revealing the answer!

Q6. A volume of 100 mL is equivalent to which one of the following volumes?

Background

Topic: Unit Conversion

This question tests your ability to convert between different metric units of volume.

Key Terms:

• 1 L = 1000 mL

• 1 kL = 1000 L

• 1 ML = 1,000,000 L

• 1 μL = 10-6 L

Step-by-Step Guidance

1. Convert 100 mL to liters: $100 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}}$.

2. Compare your result to the options given and identify the equivalent volume.

Try solving on your own before revealing the answer!

Q7. Express 50 miles per hour in units of meters per second. (1 mi = 1609 m)

Background

Topic: Unit Conversion (Speed)

This question tests your ability to convert speed from miles per hour to meters per second using unit analysis.

Key Formula:

$\text{Speed in m/s} = \text{Speed in mi/hr} \times \frac{1609 \text{ m}}{1 \text{ mi}} \times \frac{1 \text{ hr}}{3600 \text{ s}}$

Step-by-Step Guidance

1. Write the given speed: $50 \text{ mi/hr}$.

2. Multiply by the conversion factor for miles to meters: $50 \times 1609$.

3. Divide by the number of seconds in an hour: $\frac{50 \times 1609}{3600}$.

4. Simplify the expression to get the speed in m/s.

Try solving on your own before revealing the answer!

Q8. A plot of land contains 5.8 acres. How many square meters does it contain? (1.0 acre = 43,560 ft2 and 2.54 cm = 1.00 in)

Background

Topic: Area Conversion

This question tests your ability to convert area from acres to square meters, using multiple unit conversions.

Key Steps:

• 1 acre = 43,560 ft2

• 1 ft = 12 in

• 1 in = 2.54 cm

• 1 m = 100 cm

Step-by-Step Guidance

1. Multiply the number of acres by the number of square feet per acre: $5.8 \times 43,560$.

2. Convert square feet to square inches: $1 \text{ ft}^2 = (12 \text{ in})^2$.

3. Convert square inches to square centimeters: $1 \text{ in}^2 = (2.54 \text{ cm})^2$.

4. Convert square centimeters to square meters: $1 \text{ m}^2 = (100 \text{ cm})^2$.

5. Combine all conversion factors to get the area in square meters.

Try solving on your own before revealing the answer!

Q9. An oak tree was planted 22.00 years ago. How many seconds is this? (Assume a year is exactly 365 days)

Background

Topic: Time Conversion

This question tests your ability to convert years to seconds using unit analysis.

Key Steps:

• 1 year = 365 days

• 1 day = 24 hours

• 1 hour = 60 minutes

• 1 minute = 60 seconds

Step-by-Step Guidance

1. Multiply the number of years by 365 to get the number of days.

2. Multiply by 24 to get the number of hours.

3. Multiply by 60 to get the number of minutes.

4. Multiply by 60 again to get the number of seconds.

Try solving on your own before revealing the answer!

Q10. True or False: The magnitude of the sum of two vectors can not be less than either of the two vectors?

Background

Topic: Vector Addition

This question tests your understanding of vector addition and the properties of vector magnitudes.

Key Concepts:

• Vectors can add constructively or destructively depending on their directions.

• The magnitude of the sum depends on the angle between the vectors.

Step-by-Step Guidance

1. Consider two vectors of equal magnitude pointing in opposite directions. What happens to their sum?

2. Think about the triangle inequality for vectors: $|\vec{A} + \vec{B}| \leq |\vec{A}| + |\vec{B}|$.

3. Decide if the sum can ever be less than either individual vector's magnitude.

Try solving on your own before revealing the answer!

Q11. True or False: The magnitude of a vector can never be less than the magnitude of any of its components?

Background

Topic: Vector Components

This question tests your understanding of how a vector's magnitude relates to its components.

Key Concepts:

• The magnitude of a vector is always greater than or equal to the magnitude of any of its components.

• For a vector $\vec{A}$ with components $A_x$ and $A_y$, $|\vec{A}| = \sqrt{A_x^2 + A_y^2}$.

Step-by-Step Guidance

1. Recall the Pythagorean theorem for vector magnitude.

2. Consider if the magnitude can ever be less than one of its components.

Try solving on your own before revealing the answer!

Q12. A bird flies 35 miles due east of its nest looking for food. Then a scarecrow diverts it at an angle 15 degrees north of west for 20 miles. What is the bird’s final displacement vector?

Background

Topic: Vector Addition (2D)

This question tests your ability to add vectors graphically and analytically using components.

Key Steps:

• Break each displacement into x (east-west) and y (north-south) components.

• Add the components to find the resultant vector.

• Use trigonometry to find the magnitude and direction of the resultant.

Step-by-Step Guidance

1. Express the first displacement (35 miles east) as components: $x_1 = 35$, $y_1 = 0$.

2. For the second displacement (20 miles, 15° north of west), calculate $x_2$ and $y_2$ using cosine and sine:

   • $x_2 = 20 \times \cos(180° - 15°)$

   • $y_2 = 20 \times \sin(180° - 15°)$

3. Add the x-components and y-components to get the total displacement vector.

4. Calculate the magnitude and direction (angle) of the resultant vector using the Pythagorean theorem and inverse tangent.

Try solving on your own before revealing the answer!

Q13. A rock is dropped off of a 250 meter tall cliff. How long does it take to hit the bottom?

Background

Topic: Kinematics (Free Fall)

This question tests your ability to use kinematic equations for objects in free fall.

Key Formula:

$y = v_0 t + \frac{1}{2} a t^2$

• $y$ = displacement (250 m downward)

• $v_0$ = initial velocity (0 m/s, since dropped)

• $a$ = acceleration due to gravity ($9.8 \text{ m/s}^2$ downward)

Step-by-Step Guidance

1. Set up the equation for vertical displacement: $250 = 0 + \frac{1}{2} \times 9.8 \times t^2$.

2. Solve for $t^2$ by isolating it on one side of the equation.

3. Take the square root to solve for $t$.

Try solving on your own before revealing the answer!

Q14. A rock is thrown directly down off of a 250 meter tall cliff at an initial velocity of 20 meters per second. How long does it take to hit the bottom?

Background

Topic: Kinematics (Initial Velocity)

This question tests your ability to use kinematic equations when the initial velocity is not zero.

Key Formula:

$y = v_0 t + \frac{1}{2} a t^2$

• $y$ = 250 m

• $v_0$ = 20 m/s (downward)

• $a$ = 9.8 m/s2 (downward)

Step-by-Step Guidance

1. Set up the equation: $250 = 20 t + \frac{1}{2} \times 9.8 \times t^2$.

2. Rearrange the equation into standard quadratic form: $0 = \frac{1}{2} \times 9.8 \times t^2 + 20 t - 250$.

3. Use the quadratic formula to solve for $t$.

Try solving on your own before revealing the answer!

Q15. A rock is thrown at an angle of 10° above the horizontal off of a 250 meter tall cliff at an initial velocity of 15 meters per second. How long until it hits the bottom?

Background

Topic: Projectile Motion

This question tests your ability to analyze projectile motion, separating initial velocity into horizontal and vertical components.

Key Steps:

• Find the vertical component of the initial velocity: $v_{0y} = v_0 \sin(10°)$

• Use the kinematic equation for vertical displacement.

Key Formula:

$y = v_{0y} t + \frac{1}{2} a t^2$

Step-by-Step Guidance

1. Calculate $v_{0y} = 15 \times \sin(10°)$.

2. Set up the equation: $250 = v_{0y} t + \frac{1}{2} \times 9.8 \times t^2$.

3. Rearrange into quadratic form and solve for $t$ using the quadratic formula.

Try solving on your own before revealing the answer!

Q16. An astronaut stands by the rim of a crater on the moon where the acceleration of gravity is 1.62 m/s2 and there is no air. To determine the depth of the crater, she drops a rock and measures the time for it to hit the bottom. The rock takes 12.2 s to hit the bottom. How deep is the crater?

Background

Topic: Kinematics (Free Fall on the Moon)

This question tests your ability to use kinematic equations with a different gravitational acceleration.

Key Formula:

$y = v_0 t + \frac{1}{2} a t^2$

• $v_0 = 0$ (dropped)

• $a = 1.62$ m/s2

• $t = 12.2$ s

Step-by-Step Guidance

1. Set up the equation: $y = 0 + \frac{1}{2} \times 1.62 \times (12.2)^2$.

2. Calculate $(12.2)^2$ and multiply by $1.62/2$.

3. This will give you the depth of the crater in meters.

Try solving on your own before revealing the answer!

Q17. When startled, a puma can jump straight up in the air. It leaves the ground with a launch velocity of 10 meters per second. How high does it get at the top of its leap?

Background

Topic: Kinematics (Vertical Motion)

This question tests your ability to use kinematic equations to find the maximum height of a projectile.

Key Formula:

$v^2 = v_0^2 + 2 a y$

• $v = 0$ m/s (at the top)

• $v_0 = 10$ m/s (upward)

• $a = -9.8$ m/s2 (downward)

Step-by-Step Guidance

1. Set $v = 0$ and solve for $y$ in the equation $0 = (10)^2 + 2(-9.8)y$.

2. Rearrange to solve for $y$.

3. Calculate the value for $y$ to find the maximum height.

Try solving on your own before revealing the answer!