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ORELA Physics (NT308) study materials
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ORELA Physics (NT308) practice questions

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Question 1Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

In physics research, a hypothesis is best described as which of the following?

  1. a mathematical equation that summarizes observed regularities
  2. a widely accepted explanation supported by many independent experiments
  3. a testable prediction that evidence can support or refute Correct answer.
  4. a preliminary guess that cannot be evaluated experimentally

Explanation

A hypothesis is a specific, testable statement derived from a theory or observation, and experiments are designed to gather evidence that may support or contradict it. Once extensively confirmed, a hypothesis may contribute to a broader theory, but it is not itself an accepted explanation or a mathematical law.

Question 2Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

An electronic balance displays a mass as 0.0450 kg. How many significant figures are in this measurement?

  1. four
  2. two
  3. five
  4. three Correct answer.

Explanation

Leading zeros only locate the decimal point and are not significant. The digits 4, 5, and the trailing zero after the decimal are significant, so the measurement has three significant figures.

Question 3Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

Which of the following is an SI base unit used in mechanical measurements?

  1. watt
  2. joule
  3. kilogram Correct answer.
  4. newton

Explanation

The kilogram is one of the seven SI base units and measures mass. The newton, joule, and watt are derived units defined in terms of base units such as kilogram, meter, and second.

Question 4Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

Galileo Galilei's inclined-plane experiments are historically significant because they did which of the following?

  1. demonstrated that force is proportional to velocity
  2. provided quantitative evidence that falling bodies accelerate uniformly Correct answer.
  3. proved that planetary orbits are perfect circles
  4. first established that heavy objects always fall faster than light ones

Explanation

By rolling balls down inclined planes, Galileo slowed the motion enough to time it and showed that the distance traveled grows with the square of time, implying uniform acceleration. This work challenged Aristotelian ideas and helped establish experimental physics.

Question 5Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

In the philosophy of physics, which statement best distinguishes a scientific theory from a scientific law?

  1. A theory can be changed, whereas a law is permanent and never revised by scientists.
  2. A theory explains phenomena, while a law describes a consistent relationship among observations. Correct answer.
  3. A theory is supported by evidence, whereas a law is accepted without any evidence.
  4. A theory is a tentative guess, whereas a law is a proven and final fact.

Explanation

Theories and laws serve different roles: theories provide explanatory frameworks for observations, while laws state regularities often expressed mathematically. Both are supported by evidence and both can be revised when new evidence demands it.

Question 6Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

A researcher wants to test whether a new insulation material reduces heat loss. Which procedure best controls an important confounding variable?

  1. Use different amounts of insulation in each trial and compare heat loss.
  2. Use identical containers and equal temperature differences in all trials. Correct answer.
  3. Measure heat loss only once for each material.
  4. Change the thickness of the container walls between trials.

Explanation

Valid comparison requires holding constant all factors other than the variable being tested. Using identical containers and equal temperature differences prevents these factors from confounding the effect of insulation material.

Question 7Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

A wavelength is reported as 6.50 × 10² nm. What is this wavelength in meters?

  1. 6.50 × 10⁻⁹ m
  2. 6.50 × 10⁻⁶ m
  3. 6.50 × 10⁻⁵ m
  4. 6.50 × 10⁻⁷ m Correct answer.

Explanation

One nanometer equals 10⁻⁹ m, so 6.50 × 10² nm equals 6.50 × 10² × 10⁻⁹ m = 6.50 × 10⁻⁷ m. Converting units by multiplying by unity ratios preserves the physical quantity while changing the numerical value and unit.

Question 8Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

A set of repeated measurements is precise but not accurate. Which description best fits these measurements?

  1. They are close to the true value but scattered widely.
  2. They are tightly clustered but offset from the true value. Correct answer.
  3. They are scattered widely and centered on the true value.
  4. They are both close to the true value and tightly clustered.

Explanation

Precision refers to the reproducibility or closeness of repeated measurements to one another, while accuracy refers to closeness to the true value. A precise but inaccurate set is tightly grouped yet systematically offset from the accepted value.

Question 9Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

In physics, the primary purpose of peer review before publication is to do which of the following?

  1. replace the need for replication by independent scientists
  2. check that the methods and conclusions are scientifically sound Correct answer.
  3. guarantee that the results will be reproducible by any laboratory
  4. award funding to the research group

Explanation

Peer review subjects a manuscript to evaluation by independent experts who assess the clarity of methods, the validity of analysis, and whether conclusions follow from evidence. It improves quality but does not guarantee reproducibility or replace replication, and it is separate from funding decisions.

Question 10Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

A student repeatedly measures the mass of a sample and obtains values that are all 0.5 g above the accepted value. This pattern most likely indicates which of the following?

  1. random error, because the measurements vary
  2. systematic error, such as an incorrectly zeroed balance Correct answer.
  3. a blunder, because the accepted value differs from the measurements
  4. no error, because the measurements are consistent

Explanation

A consistent offset in the same direction across repeated measurements points to a systematic error, often caused by instrument calibration or a zeroing mistake. Random error would produce scatter both above and below the accepted value, while consistency does not imply absence of error.

Question 11Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

Which of the following is a derived SI unit used to express force?

  1. ampere
  2. second
  3. kilogram
  4. newton Correct answer.

Explanation

The newton (N) is the SI derived unit of force, defined as kg·m/s². The kilogram, second, and ampere are SI base units, so they are not derived units.

Question 12Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

In physics inquiry, a statement is considered scientifically testable when it

  1. is expressed with mathematical symbols
  2. has been approved by a professional society
  3. agrees with the most recent textbook
  4. can be supported or contradicted by observation Correct answer.

Explanation

Testability means that observations or experiments could count for or against the claim, which is closely tied to falsifiability. Mathematical form or approval by authorities does not by itself make a claim empirically testable.

Question 13Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

A graph plots position in meters on the vertical axis against time in seconds on the horizontal axis. The slope of the best-fit line represents

  1. velocity Correct answer.
  2. acceleration
  3. time per unit distance
  4. distance multiplied by time

Explanation

Slope equals rise over run, so its units are meters per second, which is velocity. Acceleration would require a graph of velocity versus time or a curved position–time graph.

Question 14Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

An experiment investigates whether the length of a pendulum affects its period. The pendulum length is the

  1. control variable
  2. extraneous variable
  3. independent variable Correct answer.
  4. dependent variable

Explanation

The researcher deliberately varies the length, so length is the independent variable; the period is measured as the dependent variable. Mass, release angle, and other factors should be held constant as controls.

Question 15Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

A rectangle has measured sides of 2.0 cm and 3.00 cm. Using significant-figure rules for multiplication, the area should be reported as

  1. 6.0 cm² Correct answer.
  2. 6.00 cm²
  3. 6.000 cm²
  4. 6 cm²

Explanation

The product 2.0 × 3.00 = 6.00, but multiplication limits the result to the smallest number of significant figures in the factors. The factor 2.0 has two significant figures, so the area is reported as 6.0 cm².

Question 16Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

Two lengths are measured as 5.0 ± 0.2 cm and 3.0 ± 0.1 cm. When these lengths are added, the absolute uncertainty of the sum is

  1. 0.3 cm Correct answer.
  2. 0.4 cm
  3. 0.2 cm
  4. 0.1 cm

Explanation

For addition or subtraction, absolute uncertainties add directly, so the uncertainty in the sum is 0.2 cm + 0.1 cm = 0.3 cm. The measured sum would be reported as 8.0 ± 0.3 cm.

Question 17Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

Kepler's first law refined the Copernican model by establishing that planetary orbits are

  1. perfect circles centered on Earth
  2. ellipses with the Sun at one focus Correct answer.
  3. parabolic paths determined by gravity
  4. circles centered on the Sun

Explanation

Kepler's first law states that each planet moves on an ellipse with the Sun at one focus. This replaced the assumption of perfectly circular orbits used in earlier models.

Question 18Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

Treating a car as a single point particle when analyzing its motion along a highway is best described as

  1. a falsified hypothesis
  2. a systematic measurement error
  3. a unit conversion
  4. a useful idealization Correct answer.

Explanation

A point-particle model deliberately ignores the car's size, shape, and internal structure to simplify the analysis; this is an idealization. Such models are judged by whether they make useful predictions within a stated range.

Question 19Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

A measurement procedure gives the same value when repeated in the same laboratory, but other laboratories obtain consistently different values using the same procedure. This result is

  1. neither precise nor repeatable
  2. both accurate and precise
  3. reproducible but not repeatable
  4. repeatable but not reproducible Correct answer.

Explanation

Repeatability refers to agreement among repeated measurements under the same conditions, while reproducibility refers to agreement across different laboratories or operators. The scenario shows same-laboratory agreement but cross-laboratory disagreement.

Question 20Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

A carefully performed experiment yields a result that conflicts with a well-established physical theory. The most appropriate scientific response is to

  1. ignore the result because the theory is well established
  2. verify the result and attempt independent replication Correct answer.
  3. reject the theory immediately and remove it from textbooks
  4. adjust the data until they agree with the theory

Explanation

Scientific claims are tentative and self-correcting, so an anomalous result must be scrutinized and independently replicated before it overturns a well-supported theory. Checking apparatus, assumptions, and analysis helps distinguish a real effect from error.

Question 21Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

In physics, an operational definition of a quantity is best described as one that

  1. identifies the theoretical law from which the quantity is derived
  2. specifies the procedure and instruments used to measure the quantity Correct answer.
  3. expresses the quantity as a ratio of two other quantities
  4. states the quantity in terms of SI base units only

Explanation

An operational definition ties the meaning of a physical quantity to the measurement procedure and instruments used to obtain it, so different observers can apply the same operation. It is not merely a unit expression or a theoretical derivation; those describe dimensions or relationships rather than how the quantity is measured.

Question 22Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

In scientific inquiry, which statement is an observation rather than an inference?

  1. The metal rod was heated because the experimenter wanted a larger length.
  2. The metal rod's length increased by 0.12 cm after heating. Correct answer.
  3. The metal rod will expand again if it is heated.
  4. The metal rod expanded because its particles moved faster.

Explanation

An observation is a directly measurable or perceived fact, such as a recorded length change. Explanations of why the change occurred and predictions about future behavior go beyond what was directly observed.

Question 23Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

The SI prefix nano- corresponds to which factor?

  1. 10^-9 Correct answer.
  2. 10^-6
  3. 10^9
  4. 10^-12

Explanation

The prefix nano- denotes one billionth, or 10^-9, as in a nanometer being 10^-9 meter. Micro- is 10^-6, giga- is 10^9, and pico- is 10^-12.

Question 24Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

A density is reported as 2.70 g/cm³. What is this density in kg/m³? (1 kg = 1000 g; 1 m³ = 10^6 cm³)

  1. 2.70 × 10^-3 kg/m³
  2. 2.70 × 10^6 kg/m³
  3. 2.70 × 10^3 kg/m³ Correct answer.
  4. 2.70 × 10^0 kg/m³

Explanation

Since 1 g/cm³ equals 1000 kg/m³, multiply 2.70 by 1000 to obtain 2700 kg/m³, or 2.70 × 10³ kg/m³. Equivalently, 1 g = 10^-3 kg and 1 cm³ = 10^-6 m³, so the conversion factor is 10^-3 / 10^-6 = 10³.

Question 25Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

A student measures the acceleration due to gravity as 9.60 m/s². The accepted value is 9.81 m/s². What is the percent error, to two significant figures?

  1. 2.2%
  2. 0.21%
  3. 2.1% Correct answer.
  4. 21%

Explanation

Percent error is |measured - accepted| / accepted × 100%. Here |9.60 - 9.81| / 9.81 × 100% ≈ 2.1%, using the accepted value in the denominator.

Question 26Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

On a graph, two data points have vertical error bars that do not overlap. What is the most reasonable interpretation?

  1. The two points were certainly measured with different instruments.
  2. The difference between the points is likely larger than the measurement uncertainty. Correct answer.
  3. The difference between the points is likely within measurement uncertainty.
  4. The data cannot be used because error bars are present.

Explanation

Error bars represent the uncertainty in each plotted value. If the vertical bars do not overlap, the interval allowed by the first measurement does not reach the interval allowed by the second, so the difference is likely larger than the stated uncertainty.

Question 27Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

The speed of light is about 3.00 × 10^8 m/s. Which distance does light travel in 2.0 × 10^-3 s?

  1. 6.0 × 10^5 m Correct answer.
  2. 6.0 × 10^11 m
  3. 1.5 × 10^11 m
  4. 1.5 × 10^5 m

Explanation

Distance equals speed multiplied by time: (3.00 × 10^8 m/s)(2.0 × 10^-3 s) = 6.0 × 10^5 m. Multiplying the coefficients and adding exponents for powers of ten gives the result.

Question 28Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

An equation proposes that the period T of a simple pendulum depends on length L and gravitational acceleration g according to T = 2π√(L/g). Which statement correctly checks the dimensions?

  1. L/g has units of meters, so the square root gives m; the equation is inconsistent.
  2. L/g has units of seconds, so the square root gives √s; the equation is inconsistent.
  3. L/g has units of seconds squared, so the square root gives seconds; the equation is dimensionally consistent. Correct answer.
  4. L/g has units of meters per second squared, so the square root gives m/s; the equation is inconsistent.

Explanation

L has units of meters and g has units of m/s², so L/g has units of m/(m/s²) = s². The square root then gives seconds, matching the unit of period, so the expression is dimensionally consistent.

Question 29Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

In modern physics, Noether's theorem is important because it establishes a connection between which two concepts?

  1. Wave-particle duality and the uncertainty principle
  2. Absolute space and absolute time
  3. Entropy and the arrow of time
  4. Conservation laws and continuous symmetries of a physical system Correct answer.

Explanation

Noether's theorem shows that every continuous symmetry of a physical system's action corresponds to a conserved quantity. For example, time-translation symmetry is associated with energy conservation and spatial-translation symmetry with momentum conservation.

Question 30Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

A result is published, but no independent group can reproduce it. In the context of scientific inquiry, what is the most appropriate conclusion?

  1. The result is automatically fraudulent.
  2. The result remains provisional and requires further independent verification before being treated as established. Correct answer.
  3. The original result should be accepted because it was published.
  4. The result proves the underlying theory is false.

Explanation

Scientific claims become established through independent confirmation, so a failure to reproduce makes the original result provisional rather than automatically false or fraudulent. Further investigation is needed to identify whether the discrepancy arises from error, uncontrolled conditions, or a genuine effect.

Question 31Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

James Clerk Maxwell's formulation of electromagnetism is historically significant in physics primarily because it

  1. It unified electricity, magnetism, and optics in a single field theory. Correct answer.
  2. It proved that planetary orbits are ellipses with the Sun at one focus.
  3. It supplied the first experimental evidence for the existence of the neutron.
  4. It established that energy is emitted only in discrete quantized packets.

Explanation

Maxwell's equations describe electric and magnetic fields as coupled phenomena and predict electromagnetic waves whose speed matches light. This made optics a branch of electromagnetism and influenced Einstein's relativity. The other achievements belong to different physicists and periods.

Question 32Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

A micrometer screw gauge reads 0.02 mm when its jaws are fully closed. It then reads 3.45 mm on a wire. What is the corrected wire diameter?

  1. 3.43 mm Correct answer.
  2. 3.47 mm
  3. 0.02 mm
  4. 3.45 mm

Explanation

A positive zero error means the micrometer reads too large even when closed, so the same offset must be subtracted from every measurement. Thus 3.45 mm - 0.02 mm = 3.43 mm. Zero error is a systematic effect, not a random one to be averaged away.

Question 33Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

A physics class uses a computer simulation that assumes no air resistance to predict projectile range. The prediction matches experiment poorly when a light foam ball is used. Which conclusion is most scientifically appropriate?

  1. Any difference can be removed by multiplying predictions by an untested factor.
  2. The simulation is completely worthless because it fails to match the outcome of a single experiment.
  3. The experiment must be wrong because computer simulations are based on accepted theory.
  4. The drag-free model is inadequate here because air resistance matters for the foam ball. Correct answer.

Explanation

A model is valid only within the conditions it represents, and the no-air-resistance assumption fails for a light foam ball. The appropriate response is to recognize the model's limited domain and revise or extend it, not to discard all simulation or force an arbitrary correction. Scientific models are judged by their scope and predictive usefulness.

Question 34Nature of Science (scientific inquiry, measurement, and the history and nature of physics)

A student reports g = (9.79 ± 0.05) m/s². The accepted local value is 9.81 m/s². Which interpretation is most appropriate?

  1. The stated uncertainty shows that the measuring apparatus must have been faulty.
  2. The result is inconsistent because the measured value and the accepted value are not exactly equal.
  3. The uncertainty is meaningless unless the student repeats the measurement many times.
  4. The accepted value falls inside the uncertainty interval, so the result is compatible. Correct answer.

Explanation

The reported interval is from 9.74 to 9.84 m/s², which includes the accepted 9.81 m/s². Therefore the measurement is compatible with the accepted value within its stated uncertainty; equality of central values is not required. More repetitions could reduce uncertainty but are not needed to make this compatibility judgment.

Question 35Mechanics (kinematics, Newton's laws, work, energy, momentum, and rotational motion)

A ball is released from rest and falls freely near Earth's surface. If air resistance is negligible, how long does it take to fall 45 m? Use g = 10 m/s^2.

  1. 3.0 s Correct answer.
  2. 9.0 s
  3. 4.5 s
  4. 1.5 s

Explanation

For free fall from rest, the distance is h = ½gt². Rearranging gives t = √(2h/g) = √(90/10) = √9 = 3.0 s. The other choices come from misplacing the factor of ½ or treating the distance in meters as a time in seconds.

Question 36Mechanics (kinematics, Newton's laws, work, energy, momentum, and rotational motion)

A 2.0 kg cart experiences a constant net force of 6.0 N. What is the magnitude of its acceleration?

  1. 8.0 m/s^2
  2. 0.33 m/s^2
  3. 12 m/s^2
  4. 3.0 m/s^2 Correct answer.

Explanation

Newton's second law states that net force equals mass times acceleration, so a = Fnet/m = 6.0 N / 2.0 kg = 3.0 m/s². Mass measures resistance to acceleration, so dividing by mass is required rather than multiplying or adding.

Question 37Mechanics (kinematics, Newton's laws, work, energy, momentum, and rotational motion)

A constant force of 20 N pushes a crate 5.0 m across a floor in the direction of the force. How much work does the force do on the crate?

  1. 100 J Correct answer.
  2. 25 J
  3. 4.0 J
  4. 0 J

Explanation

Work for a constant force is W = Fd cos θ, where θ is the angle between force and displacement. Because the force is in the direction of motion, cos θ = 1, so W = 20 N × 5.0 m = 100 J. Work measures energy transferred by the force.

Question 38Mechanics (kinematics, Newton's laws, work, energy, momentum, and rotational motion)

A 2.0 kg cart moving at 3.0 m/s collides with a stationary 4.0 kg cart. The carts stick together after the collision. What is their common speed immediately after the collision?

  1. 1.0 m/s Correct answer.
  2. 2.0 m/s
  3. 0.50 m/s
  4. 1.5 m/s

Explanation

In a perfectly inelastic collision, momentum is conserved but kinetic energy is not. Initial momentum is (2.0 kg)(3.0 m/s) = 6.0 kg·m/s, and the combined mass is 6.0 kg, so the final speed is 6.0/6.0 = 1.0 m/s.

Question 39Mechanics (kinematics, Newton's laws, work, energy, momentum, and rotational motion)

A ball is launched horizontally at 20 m/s from a cliff 45 m high. Ignoring air resistance, how far from the base of the cliff does the ball land? Use g = 10 m/s^2.

  1. 30 m
  2. 90 m
  3. 20 m
  4. 60 m Correct answer.

Explanation

The vertical and horizontal motions are independent. The fall time satisfies h = ½gt², giving t = √(2h/g) = √(90/10) = 3.0 s, and the horizontal speed stays 20 m/s, so the range is (20 m/s)(3.0 s) = 60 m.

Question 40Mechanics (kinematics, Newton's laws, work, energy, momentum, and rotational motion)

A 5.0 kg block on a frictionless horizontal table is connected by a light string over a frictionless pulley to a 3.0 kg hanging block. What is the acceleration of the system? Use g = 9.8 m/s^2.

  1. 3.7 m/s^2 Correct answer.
  2. 6.1 m/s^2
  3. 2.0 m/s^2
  4. 9.8 m/s^2

Explanation

The hanging block's weight, 3.0g, is the net external force accelerating both blocks, whose total mass is 8.0 kg. Thus a = (3.0 × 9.8)/8.0 = 3.675 m/s², approximately 3.7 m/s². The tension is less than the hanging weight because that block accelerates downward.

Question 41Mechanics (kinematics, Newton's laws, work, energy, momentum, and rotational motion)

A 0.50 kg ball is moving horizontally at 10 m/s. How much work must be done on the ball to bring it to rest?

  1. 25 J Correct answer.
  2. 100 J
  3. 5.0 J
  4. 50 J

Explanation

The work-energy theorem states that net work equals the change in kinetic energy. The initial kinetic energy is ½(0.50 kg)(10 m/s)² = 25 J, and the final kinetic energy is zero, so the magnitude of the work required is 25 J.

Question 42Mechanics (kinematics, Newton's laws, work, energy, momentum, and rotational motion)

A uniform solid disk has a mass of 2.0 kg and a radius of 0.50 m. What is its moment of inertia about its central axis?

  1. 0.50 kg·m^2
  2. 0.25 kg·m^2 Correct answer.
  3. 1.0 kg·m^2
  4. 0.125 kg·m^2

Explanation

For a uniform solid disk rotating about its central axis, I = ½MR². Substituting M = 2.0 kg and R = 0.50 m gives I = 0.5 × 2.0 × (0.50)² = 0.25 kg·m². Using MR² instead would incorrectly treat the disk as a thin ring.

Question 43Mechanics (kinematics, Newton's laws, work, energy, momentum, and rotational motion)

A figure skater spinning with arms extended has moment of inertia I and angular speed ω. She pulls her arms inward, reducing her moment of inertia to I/2. Ignoring external torques, what is her new angular speed?

  1. ω/2
  2. ω
  3. 4ω
  4. 2ω Correct answer.

Explanation

With no external torque, angular momentum L = Iω is conserved. If the moment of inertia becomes half its original value, the angular speed must double: (I)(ω) = (I/2)(ω′), so ω′ = 2ω. Rotational kinetic energy increases because the skater does work pulling her arms inward.

Question 44Mechanics (kinematics, Newton's laws, work, energy, momentum, and rotational motion)

A solid sphere is released from rest and rolls without slipping down an incline from a vertical height h. What is its translational speed at the bottom of the incline?

  1. √(gh)
  2. √(2gh)
  3. √(4gh/3)
  4. √(10gh/7) Correct answer.

Explanation

Conservation of energy gives mgh = ½mv² + ½Iω². For a solid sphere, I = (2/5)mR², and rolling without slipping means ω = v/R, so mgh = (7/10)mv². Solving yields v = √(10gh/7), which is less than the speed of a frictionless sliding block.

Question 45Mechanics (kinematics, Newton's laws, work, energy, momentum, and rotational motion)

A car starts from rest and accelerates uniformly at 2.0 m/s² for 5.0 s. How far does it travel during this time?

  1. 10 m
  2. 50 m
  3. 25 m Correct answer.
  4. 5.0 m

Explanation

For constant acceleration starting from rest, displacement is Δx = ½at². Substituting a = 2.0 m/s² and t = 5.0 s gives Δx = ½(2.0)(25) = 25 m.

Question 46Mechanics (kinematics, Newton's laws, work, energy, momentum, and rotational motion)

A book rests on a table. Earth exerts a downward gravitational force on the book. Which force is the Newton's third-law partner to this gravitational force?

  1. The normal force the book exerts on the table
  2. The gravitational force the book exerts on Earth Correct answer.
  3. The normal force the table exerts on the book
  4. The net force on the book when it is at rest

Explanation

Newton's third-law pairs are equal in magnitude, opposite in direction, and act on different objects, and they are the same type of force. The partner of Earth's gravitational pull on the book is the book's gravitational pull on Earth.

Question 47Mechanics (kinematics, Newton's laws, work, energy, momentum, and rotational motion)

A constant net force of 4.0 N acts for 3.0 s on a 2.0 kg cart initially at rest on a frictionless track. What is the cart's final speed?

  1. 12 m/s Correct answer.
  2. 4.0 m/s
  3. 2.0 m/s
  4. 6.0 m/s

Explanation

Impulse equals change in momentum, so FΔt = mΔv. The impulse is (4.0 N)(3.0 s) = 12 N·s, and dividing by 2.0 kg gives Δv = 6.0 m/s; starting from rest, the final speed is 6.0 m/s.

Question 48Mechanics (kinematics, Newton's laws, work, energy, momentum, and rotational motion)

A ball is launched at 20 m/s at 30° above the horizontal. Ignoring air resistance, what maximum height does it reach? Use g = 9.8 m/s².

  1. 2.6 m
  2. 20 m
  3. 10 m
  4. 5.1 m Correct answer.

Explanation

The vertical component of the launch velocity is v_y = 20 sin 30° = 10 m/s. At maximum height the vertical velocity is zero, so h = v_y²/(2g) = 100/(19.6) ≈ 5.1 m.

Question 49Mechanics (kinematics, Newton's laws, work, energy, momentum, and rotational motion)

A 4.0 kg block slides down a 30° incline. The coefficient of kinetic friction between the block and the incline is 0.20. What is the magnitude of the block's acceleration? Use g = 9.8 m/s².

  1. 4.9 m/s²
  2. 2.3 m/s²
  3. 3.2 m/s² Correct answer.
  4. 6.6 m/s²

Explanation

Along the incline, the net acceleration is a = g(sin θ − μ_k cos θ). Thus a = 9.8(0.50 − 0.20 × 0.866) ≈ 9.8(0.327) ≈ 3.2 m/s².

Question 50Mechanics (kinematics, Newton's laws, work, energy, momentum, and rotational motion)

A 0.50 kg block is released from rest at the top of a frictionless ramp and slides down a vertical height of 1.8 m before contacting a spring with k = 200 N/m. What is the maximum compression of the spring?

  1. 0.090 m
  2. 0.15 m
  3. 0.60 m
  4. 0.30 m Correct answer.

Explanation

Conservation of mechanical energy gives mgh = ½kx² at maximum compression. Solving x = sqrt(2mgh/k) = sqrt(2 × 0.50 × 9.8 × 1.8 / 200) ≈ 0.30 m.