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MTTC Physics (019) study materials
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MTTC Physics (019) practice questions

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Question 1Scientific Inquiry and Process Skills in Physics

A student uses an electronic balance to record the mass of a metal cylinder as 24.60 g. Which statement correctly describes the precision and significant figures of this recorded value?

  1. The value 24.60 g has six significant figures because every digit is counted.
  2. The trailing zero in 24.60 g is a placeholder and is not significant.
  3. The balance read to 0.1 g, and 24.60 g has three significant figures.
  4. The balance read to 0.01 g, and 24.60 g has four significant figures. Correct answer.

Explanation

In a decimal measurement, a trailing zero to the right of the decimal point is significant because it reflects the instrument's resolution. The final digit occupies the hundredths place, so the balance read to 0.01 g, and all four digits in 24.60 are significant.

Question 2Scientific Inquiry and Process Skills in Physics

Four measurements of g are 9.45, 9.46, 9.44, and 9.45 m/s²; the accepted local value is 9.81 m/s². Which description best characterizes the data set?

  1. The data are both accurate and precise.
  2. The data are accurate but not precise.
  3. The data are neither precise nor accurate.
  4. The data are precise but not accurate. Correct answer.

Explanation

Precision refers to how closely repeated measurements agree with one another, while accuracy refers to closeness to the accepted value. The four values cluster tightly within about 0.02 m/s² of each other, showing high precision, but they lie roughly 0.36 m/s² below the accepted value, showing poor accuracy.

Question 3Scientific Inquiry and Process Skills in Physics

An experiment investigates how the period of a simple pendulum depends on its length while the bob mass and release angle are held constant. Which quantity is the independent variable?

  1. Length of the pendulum Correct answer.
  2. Release angle
  3. Period of the pendulum
  4. Bob mass

Explanation

The independent variable is the quantity the experimenter deliberately changes, which here is the pendulum length. The period is the dependent variable because it is measured in response, while bob mass and release angle are controlled variables held fixed.

Question 4Scientific Inquiry and Process Skills in Physics

For a simple pendulum, theory predicts T = 2π√(L/g). To produce a straight-line graph whose slope can be used to find g, which plot should students construct?

  1. T² versus 1/L
  2. T versus L
  3. T² versus L Correct answer.
  4. T versus L²

Explanation

Squaring both sides gives T² = (4π²/g)L, which is linear in L. A plot of T² versus L therefore has slope 4π²/g, from which g can be calculated. Plotting T versus L yields a square-root curve, not a straight line.

Question 5Scientific Inquiry and Process Skills in Physics

A thermometer used in a calorimetry experiment consistently reads 1.5 °C below the true temperature at every point in its range. How should this error be classified and handled?

  1. Systematic error; calibrate the thermometer or add 1.5 °C to every reading. Correct answer.
  2. Resolution error; interpolate between the scale markings.
  3. Random error; average many readings to remove the offset.
  4. Parallax error; view the thermometer from a different angle.

Explanation

A constant offset across the entire measurement range is characteristic of a systematic error, often from calibration or zero error. Because the offset affects every reading in the same direction, averaging repeated trials will not eliminate it; calibration or applying a correction is required.

Question 6Scientific Inquiry and Process Skills in Physics

A rectangular plate measures 12.0 ± 0.1 cm by 5.0 ± 0.1 cm. Using the fractional-uncertainty rule for a product, what is the best estimate of the absolute uncertainty in the area?

  1. 1.7 cm² Correct answer.
  2. 1.2 cm²
  3. 0.2 cm²
  4. 0.5 cm²

Explanation

The area is 60 cm². The fractional uncertainties are 0.1/12.0 ≈ 0.0083 and 0.1/5.0 = 0.020; for a product they add, giving about 0.0283. Multiplying by 60 cm² yields an absolute uncertainty of about 1.7 cm².

Question 7Scientific Inquiry and Process Skills in Physics

A position-versus-time graph for a cart moving along a straight track is a straight line with slope +2.5 m/s. What physical quantity does the slope represent, and what do its units confirm?

  1. Time interval, because the horizontal axis is time.
  2. Velocity, because slope is displacement divided by time and has units m/s. Correct answer.
  3. Acceleration, because the units m/s indicate how position changes with time.
  4. Distance traveled, because slope measures total path length.

Explanation

The slope of a position-versus-time graph is the change in position divided by the change in time, which is velocity. Its units, meters per second, match velocity and confirm the interpretation. Acceleration would require the slope of a velocity-versus-time graph.

Question 8Scientific Inquiry and Process Skills in Physics

A student wants to test whether launch angle affects the range of a projectile. Which procedure best controls variables so that the result can be attributed to angle?

  1. Use projectiles of different masses for each launch angle.
  2. Vary both the launch angle and the launch speed from trial to trial.
  3. Keep launch speed, height, and mass constant; vary only angle. Correct answer.
  4. Repeat trials only at 45° and average the ranges.

Explanation

A valid test of the effect of launch angle must change that variable alone and keep all other influential factors fixed. Launch speed, launch height, and projectile mass can all affect range, so controlling them prevents confounding. Varying two factors at once would make the cause of any range difference ambiguous.

Question 9Scientific Inquiry and Process Skills in Physics

Students plot T² versus L for a simple pendulum and obtain a best-fit line with slope 4.05 s²/m and vertical intercept 0.02 s². Using g = 4π²/slope, which value of g and which interpretation of the intercept are most defensible?

  1. g ≈ 9.75 m/s²; the intercept suggests a small systematic offset. Correct answer.
  2. g ≈ 9.75 m/s²; the intercept proves the data are purely random.
  3. g ≈ 4.05 m/s²; the intercept is the pendulum's period at zero length.
  4. g ≈ 9.81 m/s²; the intercept confirms the model has no systematic effects.

Explanation

Substituting the slope gives g = 4π²/4.05 ≈ 9.75 m/s². A nonzero intercept is not predicted by the ideal T² = (4π²/g)L model, so a small positive value likely reflects a systematic offset such as an effective length correction or timing bias.

Question 10Scientific Inquiry and Process Skills in Physics

A student measures spring extension versus applied force and finds a straight line for small forces but upward curvature beyond about 8 N. Which conclusion is most defensible?

  1. The applied force is the dependent variable because it appears on the vertical axis.
  2. The linear region gives the spring constant, but Hooke's law fails beyond 8 N. Correct answer.
  3. The entire data set must be discarded because any curvature indicates a measurement blunder.
  4. Hooke's law is valid for all applied forces because the first data points are linear.

Explanation

Hooke's law, F = kx, predicts a linear force-extension relation only within the elastic limit. The slope of the linear region gives the spring constant, while the curvature at larger forces shows the model no longer applies. Curvature is a physical limitation of the spring, not automatically evidence of a blunder.

Question 11Scientific Inquiry and Process Skills in Physics

The pascal (Pa) is the SI unit of pressure, defined as one newton per square meter. Expressed in base SI units, which combination is equivalent to the pascal?

  1. kg/(m²·s²)
  2. kg·m²/s²
  3. kg·m/s²
  4. kg/(m·s²) Correct answer.

Explanation

Pressure is force per unit area, and the newton is kg·m/s². Substituting the newton into N/m² and simplifying gives kg/(m·s²).

Question 12Scientific Inquiry and Process Skills in Physics

A student investigates how the resistance of a metal wire depends on its length. Which set of quantities must be held constant so the result tests only the effect of length?

  1. Wire material, cross-sectional area, and temperature Correct answer.
  2. The current through the wire and the voltage across it, both fixed
  3. The resistance of the wire and the current through it
  4. The length of the wire and the applied voltage, both fixed

Explanation

The resistance of a wire depends on its material, length, cross-sectional area, and temperature. To isolate length as the independent variable, the other three factors must be controlled.

Question 13Scientific Inquiry and Process Skills in Physics

A student measures the period of a pendulum by timing one complete swing with a stopwatch. Which change would most effectively reduce random error in the measured period?

  1. Using the same release angle for every trial
  2. Timing 20 complete swings and dividing the total time by 20 Correct answer.
  3. Measuring the pendulum length with a meter stick to the nearest millimeter
  4. Calibrating the stopwatch against a standard clock before the trials

Explanation

Random timing error is reduced by increasing the total timed interval while keeping the same absolute reaction-time uncertainty. Timing many swings and dividing gives a smaller uncertainty per swing than timing one swing.

Question 14Scientific Inquiry and Process Skills in Physics

A light sensor measures the intensity I of light from a point source at several distances r. Theory predicts I = k/r². To obtain a straight-line graph, which quantities should be plotted?

  1. I plotted against r, with I vertical
  2. I plotted against r², with I vertical
  3. I² plotted against r, with I² vertical
  4. I plotted against 1/r², with I vertical Correct answer.

Explanation

The equation I = k/r² has the form y = kx if y is I and x is 1/r². A graph of I versus 1/r² is therefore linear, with slope k.

Question 15Scientific Inquiry and Process Skills in Physics

A student repeats a measurement 25 times and averages the results. Compared with a single measurement, the standard error of the mean is reduced by what factor, assuming only random errors?

  1. 5 Correct answer.
  2. 2.5
  3. 25
  4. √5

Explanation

The standard error of the mean is s/√N, where N is the number of independent trials. For N = 25, √25 = 5, so averaging reduces the random component of the uncertainty by a factor of 5.

Question 16Scientific Inquiry and Process Skills in Physics

A graph of applied force versus extension for a spring is a straight line through the origin with slope 24 N/m. What physical quantity does the slope represent?

  1. The elastic potential energy stored in the spring
  2. The maximum force the spring can withstand
  3. The work done in stretching the spring
  4. The spring constant of the spring Correct answer.

Explanation

For a spring obeying Hooke's law, F = kx, so a graph of F versus x has slope k. The slope is therefore the spring constant, with units of newtons per meter.

Question 17Scientific Inquiry and Process Skills in Physics

A resistance thermometer is calibrated with two known points: 100 Ω at 0 °C and 138 Ω at 100 °C. Its response is linear. What temperature corresponds to a resistance of 119 Ω?

  1. 38 °C
  2. 25 °C
  3. 75 °C
  4. 50 °C Correct answer.

Explanation

For a linear calibration, the fraction of the resistance change from 100 Ω to 138 Ω equals the fraction of the temperature change from 0 °C to 100 °C. The change is 19 Ω out of 38 Ω, or one-half, so the temperature is 50 °C.

Question 18Scientific Inquiry and Process Skills in Physics

The density of a metal cylinder is calculated from ρ = m/(πr²h). The mass has a 1.0% uncertainty, the radius has a 1.0% uncertainty, and the height has a 2.0% uncertainty. Using the worst-case fractional-uncertainty rule, what is the percent uncertainty in the calculated density?

  1. 4.0%
  2. 3.0%
  3. 5.0% Correct answer.
  4. 2.0%

Explanation

In the worst-case fractional-uncertainty rule, percent uncertainties add, and a quantity raised to a power has its percent uncertainty multiplied by that power. Here the density uncertainty is 1.0% (mass) + 2×1.0% (radius) + 2.0% (height) = 5.0%.

Question 19Scientific Inquiry and Process Skills in Physics

Two methods for measuring a physical constant give results 5.0 ± 0.3 and 5.5 ± 0.3, where the uncertainties are standard uncertainties. The two uncertainty intervals overlap. Which conclusion is best supported by these data alone?

  1. The data do not establish a statistically significant difference between the methods. Correct answer.
  2. The second method is definitely more accurate because its measured value is larger.
  3. The two methods definitely agree because their stated uncertainty intervals overlap.
  4. The first method is invalid because its stated uncertainty is not equal to zero.

Explanation

Each result is a mean with an uncertainty, and the intervals 5.0 ± 0.3 and 5.5 ± 0.3 overlap. Overlap means the observed difference is small relative to the stated uncertainties, so these data alone do not establish a significant difference.

Question 20Scientific Inquiry and Process Skills in Physics

A student rolls carts of different masses down the same ramp and concludes that heavier carts accelerate faster. The heavier carts, however, use wheels with lower friction. Which statement best describes the flaw in the conclusion?

  1. Wheel friction is a confounding variable that was not controlled. Correct answer.
  2. The ramp angle should have been changed for each cart.
  3. Mass cannot affect acceleration in any experiment.
  4. The acceleration should have been measured instead of the final speed.

Explanation

The experiment varies mass but also changes wheel friction, so friction could explain the observed acceleration difference. A valid test must keep friction the same while varying mass, otherwise the two effects are confounded.

Question 21Scientific Inquiry and Process Skills in Physics

A student investigates whether the period of a mass-spring oscillator depends on the hanging mass. In this experiment, which quantity is the independent variable?

  1. The period of oscillation
  2. The release amplitude
  3. The spring constant
  4. The hanging mass Correct answer.

Explanation

The independent variable is the quantity the experimenter deliberately changes, which here is the hanging mass. The period is the dependent variable, while spring constant and release amplitude are held constant. Identifying these roles allows valid causal conclusions.

Question 22Scientific Inquiry and Process Skills in Physics

A student times a cart with a digital stopwatch that displays to 0.01 s, but the student's reaction time is about 0.20 s. Which statement best describes the measurement uncertainty?

  1. The uncertainty is exactly 0.01 s because that is the display resolution.
  2. Reaction time dominates, giving about 0.20 s. Correct answer.
  3. The measurement is invalid because reaction time is random.
  4. The uncertainty is zero if the same student performs all trials.

Explanation

The display resolution is 0.01 s, but starting and stopping by hand introduces a larger human timing uncertainty, roughly the reaction time. Resolution sets the smallest readable increment, not the total uncertainty. Repeating trials can reduce random effects but cannot eliminate reaction-time limitations.

Question 23Scientific Inquiry and Process Skills in Physics

In an experiment measuring the acceleration of a cart on an incline with a motion sensor, which practice best improves the reliability of the result?

  1. Rounding each acceleration value to one significant figure
  2. Changing the incline angle between every trial
  3. Recording one trial after careful setup
  4. Repeating runs and averaging the accelerations Correct answer.

Explanation

Reliability refers to consistency of repeated measurements, so several runs under the same conditions followed by averaging reduce the influence of random variation. Changing the incline angle would alter the quantity being studied, and rounding to one significant figure discards information. A single trial provides no indication of scatter.

Question 24Scientific Inquiry and Process Skills in Physics

A student suspects that the period T of a pendulum obeys T = kL^n, where L is length. A graph of log T versus log L gives a straight line with slope 0.50. What relationship does this slope indicate?

  1. T is directly proportional to L.
  2. T is proportional to √L. Correct answer.
  3. T is proportional to L².
  4. T is independent of L.

Explanation

Taking logarithms of T = kL^n gives log T = n log L + log k, so the slope equals the exponent n. A slope of 0.50 means n = 1/2, which is the square-root relationship. The intercept would give log k, not the exponent.

Question 25Scientific Inquiry and Process Skills in Physics

A voltmeter consistently reads 0.30 V higher than the true voltage across its entire range. A student plots measured voltage on the vertical axis versus true voltage on the horizontal axis. What feature of the best-fit line is changed by this error?

  1. The vertical intercept increases by 0.30 V, but the slope remains 1. Correct answer.
  2. Both the slope and the intercept increase by 0.30.
  3. The points scatter randomly about a line with slope 1 and zero intercept.
  4. The slope increases by 0.30 V per volt, but the intercept remains zero.

Explanation

A constant offset makes measured voltage equal true voltage plus 0.30 V, which is a line with slope 1 and vertical intercept 0.30 V. Because the offset is the same at every reading, it shifts the line vertically rather than changing its steepness. Random scatter would produce variable deviations, not a fixed offset.

Question 26Scientific Inquiry and Process Skills in Physics

A student calculates density from mass 50.0 ± 0.5 g and volume 20.0 ± 0.4 cm³. Using the fractional-uncertainty rule for a quotient, what is the percent uncertainty in the density?

  1. 1%
  2. 2%
  3. 5%
  4. 3% Correct answer.

Explanation

For a quotient, fractional uncertainties add: (0.5/50.0) + (0.4/20.0) = 0.01 + 0.02 = 0.03. Multiplying by 100% gives a 3% uncertainty in density. The individual percent uncertainties are 1% and 2%, but they combine rather than cancel.

Question 27Scientific Inquiry and Process Skills in Physics

The activity A of a radioactive sample is measured at several times t. To test whether the data follow A = A₀e^(−λt), which graph should produce a straight line?

  1. ln A versus t Correct answer.
  2. 1/A versus t
  3. A versus t
  4. A² versus t

Explanation

Taking the natural logarithm of A = A₀e^(−λt) gives ln A = ln A₀ − λt. Thus a plot of ln A versus t is linear with slope −λ. Plotting A versus t gives an exponential curve, and neither A² nor 1/A linearizes this model.

Question 28Scientific Inquiry and Process Skills in Physics

Two methods measure g. Method A gives 9.72 ± 0.05 m/s²; Method B gives 9.83 ± 0.12 m/s². The accepted local value is 9.81 m/s². Which comparison is best supported?

  1. The two methods are equally accurate because their uncertainties overlap.
  2. Method A is both more accurate and more precise than Method B.
  3. Method A is more precise, while Method B is more accurate. Correct answer.
  4. Method B is both more accurate and more precise than Method A.

Explanation

Precision is indicated by the size of the uncertainty, so Method A with ±0.05 m/s² is more precise than Method B with ±0.12 m/s². Accuracy is closeness to the accepted value: Method B's mean 9.83 m/s² is closer to 9.81 m/s² than Method A's 9.72 m/s². Overlap of uncertainties does not make their central values equally accurate.

Question 29Scientific Inquiry and Process Skills in Physics

A student measures the count rate from a point radioactive source at several distances to test the inverse-square law, but the room background count rate is significant. Which procedure best isolates the distance dependence?

  1. Shorten each counting interval to reduce the background contribution.
  2. Increase the source activity until the detector saturates.
  3. Subtract the source-removed background count rate from each measurement. Correct answer.
  4. Use only the farthest distances where the count rate is small.

Explanation

The detector records source plus background, so subtracting a separately measured background leaves an estimate of the source contribution alone. Changing source activity or counting time does not remove the background count. Using only far distances reduces signal and makes background relatively more important.

Question 30Scientific Inquiry and Process Skills in Physics

A graph of applied force F versus acceleration a for a cart is a straight line with slope 0.50 kg and vertical intercept 0.20 N. If the intercept represents a constant friction force, what are the cart's mass and the friction force magnitude?

  1. 0.50 kg and 0.20 N Correct answer.
  2. 0.50 kg and 0.10 N
  3. 0.40 kg and 0.20 N
  4. 0.20 kg and 0.50 N

Explanation

For F = ma + f, a plot of applied force versus acceleration has slope equal to mass and vertical intercept equal to the constant friction force. The slope 0.50 kg gives the cart mass, and the intercept 0.20 N gives the friction magnitude. The intercept is not subtracted from the slope.

Question 31Scientific Inquiry and Process Skills in Physics

A student records three lengths as 12.11 cm, 0.3 cm, and 1.234 cm. When the three values are added, to how many decimal places should the sum be reported?

  1. Zero decimal places
  2. Two decimal places
  3. Three decimal places
  4. One decimal place Correct answer.

Explanation

For addition and subtraction, the result is limited by the term with the fewest decimal places. The value 0.3 cm has one decimal place, so the sum should be rounded to one decimal place, giving 13.6 cm.

Question 32Scientific Inquiry and Process Skills in Physics

An analog voltmeter has a smallest scale division of 0.2 V. A careful student takes a single reading. What is the most appropriate uncertainty to assign to that reading due to the scale resolution?

  1. ±0.05 V
  2. ±0.1 V Correct answer.
  3. ±0.2 V
  4. ±0.01 V

Explanation

For a single reading on an analog scale, the resolution uncertainty is commonly taken as half the smallest division. Half of 0.2 V is 0.1 V, so the reading should be reported with an uncertainty of about ±0.1 V.

Question 33Scientific Inquiry and Process Skills in Physics

A student needs to determine the volume of a small, irregularly shaped metal object. Which method is most appropriate for this measurement?

  1. Weigh the object on a balance and assume a density
  2. Use water displacement in a graduated cylinder Correct answer.
  3. Measure its dimensions with a ruler and use a geometric formula
  4. Estimate its volume by comparing it with a known cube

Explanation

For an irregular solid, direct geometric measurement is unreliable because no simple formula applies. Water displacement measures the volume of fluid pushed aside, which equals the object's volume when it is fully submerged and does not dissolve.

Question 34Scientific Inquiry and Process Skills in Physics

A student measures two lengths as 5.0 ± 0.1 cm and 3.0 ± 0.2 cm. The two lengths are added. What is the correct reported value for the sum and its absolute uncertainty?

  1. 8.0 ± 0.3 cm Correct answer.
  2. 8.0 ± 0.1 cm
  3. 8.0 ± 0.2 cm
  4. 8.0 ± 0.4 cm

Explanation

When independent quantities are added or subtracted, their absolute uncertainties add. The sum is 8.0 cm, and the uncertainty is 0.1 cm + 0.2 cm = 0.3 cm, so the result is 8.0 ± 0.3 cm.

Question 35Scientific Inquiry and Process Skills in Physics

A student tests the simple-pendulum relationship T = 2π√(L/g). Which graph would produce a straight line whose slope equals 2π/√g?

  1. T² against L
  2. T against √L Correct answer.
  3. T against 1/√L
  4. T against L

Explanation

Taking the square root of both sides gives T = (2π/√g)√L. Therefore a graph of T versus √L is a straight line through the origin with slope 2π/√g.

Question 36Scientific Inquiry and Process Skills in Physics

In a photoelectric-effect experiment, a graph of the maximum kinetic energy of emitted electrons versus the frequency of incident light is a straight line. What physical quantity does the slope of this graph represent?

  1. The charge of an electron
  2. Planck's constant Correct answer.
  3. The work function of the metal
  4. The threshold frequency of the metal

Explanation

The photoelectric equation is K_max = hf − φ, which has the form y = mx + b with slope h. Thus the slope of K_max versus frequency is Planck's constant.

Question 37Scientific Inquiry and Process Skills in Physics

A student makes five measurements of the acceleration due to gravity: 9.81, 9.79, 9.80, 9.82, and 9.45 m/s². What is the most appropriate first step in analyzing these data?

  1. Calculate the mean of all five values without examining the 9.45 m/s² value for a possible problem
  2. Replace the 9.45 m/s² value with the average of the other four values before analysis
  3. Discard the 9.45 m/s² value immediately because it is the smallest of the five readings
  4. Check whether the 9.45 m/s² value arose from a procedural error before excluding it Correct answer.

Explanation

An outlier should not be removed automatically; the student should first check the measurement procedure, recording, or conditions for a known problem. If no assignable cause is found, the value should be retained and analyzed with appropriate statistics.

Question 38Scientific Inquiry and Process Skills in Physics

A student must estimate the thickness of a single sheet of paper taken from a 500-sheet stack that is measured to be 5.0 cm thick. Which procedure gives the best precision?

  1. Measure ten sheets with a millimeter ruler and divide by ten
  2. Measure one sheet directly with a millimeter ruler
  3. Divide the stack thickness by 500 Correct answer.
  4. Measure the mass of one sheet and use the paper's density

Explanation

Dividing the stack thickness by the number of sheets averages the small thickness over many sheets, greatly improving precision. A single sheet is thinner than the smallest division of an ordinary ruler, so direct measurement is unreliable.

Question 39Scientific Inquiry and Process Skills in Physics

A student plots T² versus L for a simple pendulum and obtains slope 4.05 s²/m. The meterstick used for L is stretched, so every recorded length is 1.0% larger than the true length. What value of g does the student calculate, and is it larger or smaller than the true value?

  1. 9.75 m/s²; it is smaller than the true value
  2. 9.75 m/s²; it is larger than the true value Correct answer.
  3. 9.65 m/s²; it is smaller than the true value
  4. 9.65 m/s²; it is larger than the true value

Explanation

The stretched ruler makes each recorded length 1% too large, so the fitted slope is 1% too small. The student's calculated g = 4π²/slope is therefore 1% too large; with slope 4.05 s²/m, the uncorrected value is about 9.75 m/s².

Question 40Scientific Inquiry and Process Skills in Physics

A student measures pendulum length from the worn end of a ruler, so every recorded length is 0.5 cm shorter than the true length. The student plots T² versus recorded length L and fits a straight line. How does this systematic error affect the slope and the calculated value of g?

  1. The slope is too large, so g is underestimated
  2. The slope is too small, so g is overestimated
  3. The slope is unchanged, so g is unaffected Correct answer.
  4. The slope becomes zero, so g cannot be determined

Explanation

A constant error in every length shifts all L values by the same amount. On a graph of T² versus L, this changes only the intercept, not the slope, and the slope 4π²/g is what determines g. Therefore g remains unaffected, although the intercept is shifted.

Question 41Mechanics (Motion, Forces, Energy, Momentum)

A cart on a straight track moves at 12 m/s and then accelerates uniformly at 3.0 m/s² in the direction of motion for 6.0 s. What is the cart's displacement during this 6.0 s interval?

  1. 108 m
  2. 126 m Correct answer.
  3. 180 m
  4. 72 m

Explanation

For uniform acceleration, displacement is x = v₀t + ½at². Substituting gives (12)(6.0) + 0.5(3.0)(6.0)² = 72 + 54 = 126 m. Checking with average velocity, the speed rises from 12 m/s to 30 m/s, so v_avg = 21 m/s over 6.0 s, which again gives 126 m.

Question 42Mechanics (Motion, Forces, Energy, Momentum)

A rocket fires its engine in deep space, far from any planet or atmosphere. Which statement best explains why the rocket accelerates forward?

  1. As fuel burns the rocket's mass decreases, so it accelerates forward without any external force.
  2. The engine pushes against the surrounding vacuum, generating forward thrust.
  3. The rocket pushes exhaust backward, and the exhaust pushes the rocket forward with an equal-magnitude force. Correct answer.
  4. The exhaust gas pushes against empty space, and space pushes back on the rocket.

Explanation

Newton's third law pairs the force the rocket exerts on the expelled gas with the equal and opposite force the gas exerts on the rocket. Because the gas leaves at high speed, this reaction force acts continuously and accelerates the rocket. No surrounding medium is needed, since the interacting bodies are the rocket and its own propellant.

Question 43Mechanics (Motion, Forces, Energy, Momentum)

A 0.50 kg ball moving horizontally at 8.0 m/s strikes a wall and rebounds along the same line at 6.0 m/s. What is the magnitude of the change in the ball's momentum?

  1. 14 kg·m/s
  2. 1.0 kg·m/s
  3. 4.0 kg·m/s
  4. 7.0 kg·m/s Correct answer.

Explanation

Momentum is a vector, so the reversal changes the sign. Taking the initial direction as positive, Δp = m(v_f − v_i) = 0.50(−6.0 − 8.0) = −7.0 kg·m/s, whose magnitude is 7.0 kg·m/s.

Question 44Mechanics (Motion, Forces, Energy, Momentum)

A ball rolls off a horizontal cliff at 15 m/s and lands 45 m below the launch point. Ignoring air resistance and using g = 10 m/s², how far horizontally from the base of the cliff does the ball land?

  1. 30 m
  2. 15 m
  3. 60 m
  4. 45 m Correct answer.

Explanation

The vertical motion alone fixes the flight time: h = ½gt², so t = √(2 × 45/10) = 3.0 s. Horizontal velocity stays constant at 15 m/s, so the range is (15)(3.0) = 45 m.

Question 45Mechanics (Motion, Forces, Energy, Momentum)

A 4.0 kg block starts from rest and slides 5.0 m down a 30° incline while a constant 6.0 N friction force acts on it. Using g = 9.8 m/s², what is the block's speed at the bottom?

  1. 9.1 m/s
  2. 7.0 m/s
  3. 3.4 m/s
  4. 5.8 m/s Correct answer.

Explanation

The vertical drop is 5.0 sin 30° = 2.5 m, so gravity supplies mgh = (4.0)(9.8)(2.5) = 98 J. Friction removes (6.0)(5.0) = 30 J, leaving 68 J of kinetic energy, and v = √(2 × 68/4.0) ≈ 5.8 m/s.

Question 46Mechanics (Motion, Forces, Energy, Momentum)

A 1200 kg car travels at a constant 20 m/s around a flat, unbanked curve of radius 50 m. What minimum coefficient of static friction between the tires and the road is required?

  1. 0.82 Correct answer.
  2. 1.6
  3. 0.41
  4. 0.082

Explanation

The needed centripetal acceleration is v²/r = (20)²/50 = 8.0 m/s². Static friction is the only horizontal force, so μ_s mg = mv²/r, giving μ_s = 8.0/9.8 ≈ 0.82.

Question 47Mechanics (Motion, Forces, Energy, Momentum)

A 2.0 kg cart moving at 3.0 m/s collides with a 4.0 kg cart at rest, and the two stick together. What fraction of the initial kinetic energy is lost in the collision?

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

Explanation

Initial momentum is (2.0)(3.0) = 6.0 kg·m/s, so the combined 6.0 kg moves at 1.0 m/s after the collision. Initial kinetic energy is 9.0 J and final kinetic energy is 3.0 J, so 6.0 J of the 9.0 J is lost, which is two-thirds.

Question 48Mechanics (Motion, Forces, Energy, Momentum)

Two blocks, 5.0 kg and 3.0 kg, hang from opposite ends of a light string that passes over a frictionless pulley. Using g = 9.8 m/s², what is the magnitude of the blocks' acceleration?

  1. 9.8 m/s²
  2. 2.5 m/s² Correct answer.
  3. 1.2 m/s²
  4. 3.9 m/s²

Explanation

The net driving force is the weight difference, (5.0 − 3.0)(9.8) = 19.6 N, and the total mass being accelerated is 8.0 kg. Thus a = 19.6/8.0 ≈ 2.5 m/s², which is less than free fall because both blocks must move together.

Question 49Mechanics (Motion, Forces, Energy, Momentum)

A solid sphere rolls without slipping down an incline. What fraction of the sphere's total kinetic energy is rotational?

  1. 2/5
  2. 2/7 Correct answer.
  3. 5/7
  4. 1/3

Explanation

For a solid sphere I = (2/5)mR², and rolling without slipping means ω = v/R. The rotational fraction is (½Iω²)/(½mv² + ½Iω²) = (2/5)/(1 + 2/5) = 2/7.

Question 50Mechanics (Motion, Forces, Energy, Momentum)

A 0.50 kg block is pressed against a spring of constant 400 N/m, compressing it 0.20 m. The region under the spring is frictionless, but the surface beyond the spring's equilibrium position has μ_k = 0.25. Using g = 10 m/s², how far does the block slide on the rough surface before stopping?

  1. 6.4 m Correct answer.
  2. 12.8 m
  3. 8.0 m
  4. 3.2 m

Explanation

The compressed spring stores ½kx² = ½(400)(0.20)² = 8.0 J, all of which becomes kinetic energy at the equilibrium position. On the rough surface friction removes μ_k mg = (0.25)(0.50)(10) = 1.25 N per meter, so the stopping distance is 8.0/1.25 = 6.4 m.