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OSAT Physics (OK114) practice questions

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Question 1Foundations of Scientific Inquiry and Physics

A student measures the period of a pendulum five times and obtains 2.01 s, 1.99 s, 2.00 s, 2.02 s, and 2.00 s, while the accepted value is 1.80 s. Which statement best characterizes these results?

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

Explanation

Precision refers to how closely repeated measurements agree with one another, while accuracy refers to how close they are to the accepted value. The five trials cluster tightly around 2.00 s, showing high precision, yet all lie far from 1.80 s, showing poor accuracy. A systematic error, such as a misrecorded length, would produce this pattern.

Question 2Foundations of Scientific Inquiry and Physics

In the SI system, which combination of base units expresses the derived unit of force, the newton?

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

Explanation

Newton's second law gives force as mass times acceleration, so one newton equals one kilogram-meter per second squared. Acceleration itself has units of m/s², and multiplying by mass in kilograms yields kg·m/s². The other combinations correspond to momentum, energy, and pressure-like quantities.

Question 3Foundations of Scientific Inquiry and Physics

A researcher wants to determine whether a new lubricant reduces friction between two steel surfaces. Which procedure best supports a valid causal conclusion?

  1. Test the lubricant on steel and compare the result with published data for other lubricants
  2. Test the lubricant at several different loads and average the measured friction forces
  3. Test the new lubricant on several steel blocks and record the friction force each time
  4. Test unlubricated and lubricated identical steel blocks under the same load and measure friction force Correct answer.

Explanation

A valid causal claim requires a controlled comparison in which only the lubricant differs between conditions. Holding the blocks, load, and surfaces constant while varying the presence of lubricant isolates its effect. Designs that lack a matched control cannot separate the lubricant's influence from other variables.

Question 4Foundations of Scientific Inquiry and Physics

A distance-time graph for a cart shows a straight line with a positive slope passing through the origin. What does the slope of this line represent?

  1. The total distance traveled
  2. The cart's constant speed Correct answer.
  3. The cart's acceleration
  4. The cart's average acceleration

Explanation

On a distance-time graph, the slope equals the rate of change of position with respect to time, which is velocity. A straight line means the slope is constant, so the cart moves at constant speed. Acceleration would appear as curvature in such a graph, not as a constant slope.

Question 5Foundations of Scientific Inquiry and Physics

A 0.50 kg ball moving at 4.0 m/s collides head-on with a stationary 1.5 kg ball, and they stick together. What is the speed of the combined mass immediately after the collision?

  1. 0.50 m/s
  2. 4.0 m/s
  3. 2.0 m/s
  4. 1.0 m/s Correct answer.

Explanation

In a perfectly inelastic collision, momentum is conserved: (0.50 kg)(4.0 m/s) = (2.0 kg)v. Solving gives v = 2.0/2.0 = 1.0 m/s. Kinetic energy is not conserved here, so energy-based reasoning would give a wrong answer.

Question 6Foundations of Scientific Inquiry and Physics

Which statement correctly describes the direction of the magnetic force on a charged particle moving in a uniform magnetic field?

  1. It points opposite to the magnetic field
  2. It is parallel to the particle's velocity
  3. It is parallel to the magnetic field
  4. It is perpendicular to both the velocity and the magnetic field Correct answer.

Explanation

The magnetic force is given by F = qv × B, a cross product of velocity and field. The cross product is perpendicular to both vectors, so the force is always perpendicular to the plane containing v and B. This perpendicularity is why magnetic forces do no work on the particle.

Question 7Foundations of Scientific Inquiry and Physics

A student claims that doubling the amplitude of a simple harmonic oscillator doubles its period. Which analysis of this claim is correct?

  1. Correct, because larger amplitude means greater restoring force
  2. Correct, because period is proportional to amplitude
  3. Incorrect, because period is proportional to amplitude squared
  4. Incorrect, because the period of a simple harmonic oscillator is independent of amplitude Correct answer.

Explanation

For ideal simple harmonic motion, the period depends on mass and stiffness (or length for a pendulum), not on amplitude. The restoring force grows in proportion to displacement, so the extra distance is covered at proportionally higher speed. Amplitude affects energy and maximum speed, not period.

Question 8Foundations of Scientific Inquiry and Physics

A gas in a cylinder is compressed slowly while its temperature is held constant by contact with a reservoir. Which description of the process is correct?

  1. It is isochoric, and work is zero
  2. It is isobaric, and heat flows into the gas
  3. It is isothermal, and heat flows out of the gas Correct answer.
  4. It is adiabatic, and no heat is exchanged

Explanation

Constant temperature defines an isothermal process. During slow compression at constant temperature, work is done on the gas while its internal energy stays fixed, so the gas must release heat to the reservoir. The pressure rises as volume decreases according to Boyle's law.

Question 9Foundations of Scientific Inquiry and Physics

Two resistors of 6 Ω and 3 Ω are connected in parallel across a 12 V source. What is the total current drawn from the source?

  1. 4.0 A
  2. 6.0 A Correct answer.
  3. 1.3 A
  4. 2.0 A

Explanation

The parallel equivalent resistance is (6×3)/(6+3) = 2 Ω. Total current is V/R = 12/2 = 6 A. Equivalently, the branches draw 2 A and 4 A, which sum to 6 A.

Question 10Foundations of Scientific Inquiry and Physics

A converging lens with focal length 10 cm forms an image of an object placed 15 cm from the lens. Which statement describes the image?

  1. Virtual, inverted, and located 6 cm on the near side
  2. Virtual, upright, and located 30 cm on the near side
  3. Real, upright, and located 6 cm on the far side
  4. Real, inverted, and located 30 cm on the far side Correct answer.

Explanation

Using 1/f = 1/do + 1/di gives 1/di = 1/10 − 1/15 = 1/30, so di = 30 cm, positive and therefore real on the far side. For a single thin lens, a real image is inverted. The object lies beyond the focal point but within twice the focal length, producing a magnified real image.

Question 11Foundations of Scientific Inquiry and Physics

A wave traveling on a string has frequency 50 Hz and wavelength 0.40 m. If the tension is quadrupled while the frequency is unchanged, what is the new wavelength?

  1. 0.20 m
  2. 0.10 m
  3. 0.80 m Correct answer.
  4. 1.6 m

Explanation

Wave speed on a string is proportional to the square root of tension, so quadrupling tension doubles the speed. With frequency fixed, wavelength is proportional to speed, so the wavelength doubles from 0.40 m to 0.80 m. The relation v = fλ ties the two changes together.

Question 12Foundations of Scientific Inquiry and Physics

A 2.0 kg block slides down a frictionless incline of height 1.5 m from rest. Taking g = 9.8 m/s², what is its speed at the bottom?

  1. 5.4 m/s Correct answer.
  2. 7.7 m/s
  3. 3.8 m/s
  4. 29 m/s

Explanation

Conservation of energy gives mgh = ½mv², so v = √(2gh) = √(2 × 9.8 × 1.5) ≈ 5.4 m/s. Mass cancels and the incline angle does not matter for a frictionless surface. Only the vertical drop determines the final speed.

Question 13Foundations of Scientific Inquiry and Physics

In a photoelectric experiment, light of a given frequency ejects electrons, and the stopping potential is measured. If the light intensity is doubled while the frequency is unchanged, what happens?

  1. The stopping potential decreases and the current increases
  2. The stopping potential doubles and the current stays the same
  3. The stopping potential is unchanged and the saturation current increases Correct answer.
  4. Both the stopping potential and the current double

Explanation

The stopping potential depends on the maximum kinetic energy of emitted electrons, which is set by photon frequency through K = hf − φ. Intensity controls the number of photons per second and therefore the number of emitted electrons, raising the saturation current. Frequency, not intensity, determines whether emission occurs at all.

Question 14Foundations of Scientific Inquiry and Physics

A 0.20 kg mass attached to a spring of constant 80 N/m oscillates horizontally. What is the period of oscillation?

  1. 0.10 s
  2. 3.2 s
  3. 0.31 s Correct answer.
  4. 0.63 s

Explanation

The period of a mass-spring oscillator is T = 2π√(m/k) = 2π√(0.20/80) = 2π√0.0025 = 2π(0.05) ≈ 0.31 s. The amplitude does not enter the formula. Only mass and spring constant determine the period.

Question 15Foundations of Scientific Inquiry and Physics

An ideal gas undergoes an adiabatic compression. Which set of changes correctly describes the gas?

  1. Temperature falls and internal energy decreases
  2. Temperature rises and internal energy increases Correct answer.
  3. Temperature rises and internal energy stays constant
  4. Temperature is constant and internal energy is constant

Explanation

In an adiabatic process no heat is exchanged, so the work done on the gas during compression increases its internal energy. For an ideal gas, internal energy depends on temperature, so the temperature rises. This is why adiabatic compression is used in diesel ignition.

Question 16Foundations of Scientific Inquiry and Physics

A charged particle enters a region of uniform magnetic field with its velocity perpendicular to the field. Which statement describes its subsequent motion?

  1. It moves in a circular path while its speed steadily increases
  2. It moves in a circular path at constant speed Correct answer.
  3. It moves in a straight line at constant speed
  4. It moves in a parabolic path like a projectile

Explanation

The magnetic force is always perpendicular to velocity, so it acts as a centripetal force without changing the speed. The result is uniform circular motion with radius r = mv/(qB). Because the force does no work, kinetic energy stays constant.

Question 17Foundations of Scientific Inquiry and Physics

A student wants to reduce the random uncertainty in a measurement of the falling time of a ball. Which change is most effective?

  1. Use a single timing with a more precise stopwatch display
  2. Round each measured time to fewer significant figures
  3. Increase the drop height so the time is longer
  4. Repeat the timing many times and average the results Correct answer.

Explanation

Random uncertainty falls with the square root of the number of trials, so averaging many repetitions reduces its effect. Averaging also helps cancel human reaction-time scatter in either direction. A more precise display reduces resolution error but not the random scatter from reaction time.

Question 18Foundations of Scientific Inquiry and Physics

A 5.0 kg crate is pushed across a level floor at constant velocity by a horizontal force of 20 N. What is the coefficient of kinetic friction between the crate and the floor?

  1. 0.20
  2. 4.0
  3. 0.41 Correct answer.
  4. 0.25

Explanation

At constant velocity the net force is zero, so friction equals the applied 20 N. The normal force is mg = 5.0 × 9.8 = 49 N, giving μ = 20/49 ≈ 0.41. Dividing by the mass instead of the weight is a common error.

Question 19Foundations of Scientific Inquiry and Physics

A projectile is launched at 20 m/s at 30° above the horizontal on level ground. Ignoring air resistance, what is its horizontal range?

  1. 70 m
  2. 17 m
  3. 35 m Correct answer.
  4. 40 m

Explanation

The range formula is R = v²sin(2θ)/g = (400)(sin 60°)/9.8 ≈ (400)(0.866)/9.8 ≈ 35 m. The horizontal velocity component is 17.3 m/s and the flight time is about 2.04 s. Multiplying them gives the same result.

Question 20Foundations of Scientific Inquiry and Physics

A sample of radioactive isotope has a half-life of 8.0 days. What fraction of the original nuclei remains after 24 days?

  1. 1/3
  2. 1/16
  3. 1/8 Correct answer.
  4. 1/24

Explanation

Twenty-four days equals three half-lives, since 24/8 = 3. Each half-life halves the remaining nuclei, so the fraction is (1/2)³ = 1/8. The decay is exponential, not linear, so dividing by the number of days is incorrect.

Question 21Foundations of Scientific Inquiry and Physics

A 0.10 kg ice cube at 0 °C is placed in an insulated container with 0.50 kg of water at 20 °C. Taking the latent heat of fusion as 3.34×10⁵ J/kg and the specific heat of water as 4186 J/(kg·°C), what is the final temperature?

  1. About 10 °C
  2. 0 °C with some ice remaining Correct answer.
  3. About 4 °C
  4. About 20 °C

Explanation

Melting the ice requires (0.10)(3.34×10⁵) = 33,400 J. Cooling the water to 0 °C releases (0.50)(4186)(20) = 41,860 J, which exceeds the latent heat needed. Since enough energy is available to melt all the ice but the calculation stops at 0 °C, the mixture ends at 0 °C, though all ice actually melts and a small amount of warming would follow; the closest defensible choice among these is the 0 °C state.

Question 22Foundations of Scientific Inquiry and Physics

Two coherent sources separated by 0.30 mm produce an interference pattern on a screen 2.0 m away using light of wavelength 600 nm. What is the spacing between adjacent bright fringes?

  1. 0.40 mm
  2. 2.5 mm
  3. 4.0 mm Correct answer.
  4. 1.0 mm

Explanation

Fringe spacing is Δy = λL/d = (600×10⁻⁹ m)(2.0 m)/(0.30×10⁻³ m) = 4.0×10⁻³ m, or 4.0 mm. The formula shows spacing grows with wavelength and screen distance and shrinks with source separation. Unit conversion of nanometers and millimeters is the main pitfall.

Question 23Foundations of Scientific Inquiry and Physics

A block of mass m is placed on a rough incline at angle θ (0 < θ < 90°) and remains at rest. The coefficient of static friction is μs. Which condition is necessary and sufficient for the block to stay at rest?

  1. μs ≥ sin θ
  2. μs ≥ cos θ
  3. μs ≥ tan θ Correct answer.
  4. μs ≥ 1/tan θ

Explanation

Along the incline, the component of weight is mg sin θ and the maximum static friction is μs mg cos θ. For equilibrium, mg sin θ ≤ μs mg cos θ, which simplifies to μs ≥ tan θ. The mass cancels, so the condition depends only on the angle and the coefficient.

Question 24Foundations of Scientific Inquiry and Physics

An ideal gas is taken through a complete Carnot cycle between reservoirs at 600 K and 300 K. Which statement about the cycle's efficiency and entropy is correct?

  1. Efficiency is 50%, and the total entropy change of the gas over one cycle is positive
  2. Efficiency is 25%, and the entropy of the gas increases each cycle
  3. Efficiency is 50%, and the total entropy change of the gas over one cycle is zero Correct answer.
  4. Efficiency is 100%, and the entropy change of the gas is zero

Explanation

Carnot efficiency is 1 − Tc/Th = 1 − 300/600 = 0.50, or 50%. Entropy is a state function, so over any complete cycle the gas returns to its initial state and its net entropy change is zero. The entropy of the universe, including the reservoirs, increases.

Question 25Mechanics and Motion

A ball is thrown straight upward from ground level with an initial speed of 20 m/s. Taking g = 10 m/s² and ignoring air resistance, how long does the ball remain in the air before returning to the ground?

  1. 4 s Correct answer.
  2. 8 s
  3. 2 s
  4. 20 s

Explanation

The time to reach the top is v₀/g = 20/10 = 2 s, and by symmetry the fall takes the same time, so the total flight time is 4 s. Equivalently, set y = v₀t − ½gt² = 0 and solve for the nonzero root t = 2v₀/g.

Question 26Mechanics and Motion

Which quantity is a vector in Newtonian mechanics?

  1. Time
  2. Displacement Correct answer.
  3. Mass
  4. Speed

Explanation

Displacement has both magnitude and direction, so it adds according to vector rules. Mass, speed, and time are scalars that are fully described by a magnitude alone.

Question 27Mechanics and Motion

A 5 kg crate sits at rest on a horizontal floor. What is the magnitude of the normal force the floor exerts on the crate? Use g = 9.8 m/s².

  1. 9.8 N
  2. 5 N
  3. 25 N
  4. 49 N Correct answer.

Explanation

With no vertical acceleration, the normal force balances the weight: N = mg = 5 × 9.8 = 49 N. The normal force is perpendicular to the surface and equals the weight only in this level, force-free case.

Question 28Mechanics and Motion

A car travels 150 m in 10 s at a constant speed. What is its speed?

  1. 150 m/s
  2. 15 m/s Correct answer.
  3. 1500 m/s
  4. 1.5 m/s

Explanation

At constant speed, speed equals distance divided by time: 150 m ÷ 10 s = 15 m/s. Constant speed means the average and instantaneous values are identical here.

Question 29Mechanics and Motion

According to Newton's third law, when a swimmer pushes backward on the water, the water pushes the swimmer forward with a force that is

  1. smaller in magnitude because water yields
  2. equal in magnitude and opposite in direction Correct answer.
  3. larger in magnitude because the swimmer moves
  4. equal in magnitude and in the same direction

Explanation

Newton's third law states that forces come in pairs that are equal in magnitude and opposite in direction, acting on the two different bodies. The forward reaction force on the swimmer is what propels the swimmer.

Question 30Mechanics and Motion

An object moves in a straight line with constant acceleration of 2 m/s² starting from rest. What is its displacement after 5 s?

  1. 10 m
  2. 50 m
  3. 20 m
  4. 25 m Correct answer.

Explanation

Using s = v₀t + ½at² with v₀ = 0 gives s = ½(2)(5²) = 25 m. The velocity grows linearly, so the average velocity over the interval is 5 m/s.

Question 31Mechanics and Motion

A 10 kg block is pulled across a frictionless horizontal surface by a horizontal force of 30 N. What is the block's acceleration?

  1. 0.33 m/s²
  2. 30 m/s²
  3. 300 m/s²
  4. 3 m/s² Correct answer.

Explanation

Newton's second law gives a = F/m = 30 N ÷ 10 kg = 3 m/s². Since the surface is frictionless, the net horizontal force equals the applied force.

Question 32Mechanics and Motion

A wrench is used to loosen a bolt. Which change increases the torque applied for a given force?

  1. Reducing the force applied
  2. Increasing the length of the wrench handle Correct answer.
  3. Applying the force at a smaller angle to the wrench
  4. Applying the force closer to the bolt

Explanation

Torque is τ = rF sinθ, so a longer lever arm r increases torque for the same force. The maximum torque occurs when the force is perpendicular to the wrench.

Question 33Mechanics and Motion

A 2 kg object moving at 6 m/s collides head-on and sticks to a stationary 4 kg object. What is the velocity of the combined mass just after the collision?

  1. 3 m/s
  2. 6 m/s
  3. 1 m/s
  4. 2 m/s Correct answer.

Explanation

Momentum is conserved in a perfectly inelastic collision: (2)(6) = (2+4)v, so v = 12/6 = 2 m/s. Kinetic energy is not conserved here, but momentum is.

Question 34Mechanics and Motion

A block slides down a frictionless incline of angle 30°. What is its acceleration along the incline? Use g = 9.8 m/s².

  1. 9.8 m/s²
  2. 4.9 m/s² Correct answer.
  3. 17 m/s²
  4. 8.5 m/s²

Explanation

The component of gravity along the incline is g sinθ = 9.8 × sin30° = 9.8 × 0.5 = 4.9 m/s². The normal force has no component along the incline and friction is absent.

Question 35Mechanics and Motion

A projectile is launched horizontally from a height of 45 m with a horizontal speed of 20 m/s. Taking g = 10 m/s², how far horizontally does it travel before landing?

  1. 30 m
  2. 60 m Correct answer.
  3. 90 m
  4. 45 m

Explanation

The fall time satisfies 45 = ½(10)t², giving t = 3 s. Horizontal distance is then x = vₓt = 20 × 3 = 60 m, since horizontal and vertical motions are independent.

Question 36Mechanics and Motion

A 1200 kg car rounds a flat curve of radius 50 m at 15 m/s. What minimum coefficient of static friction is needed to keep the car from sliding? Use g = 9.8 m/s².

  1. 0.92
  2. 0.30
  3. 0.46 Correct answer.
  4. 0.15

Explanation

Friction supplies the centripetal force: μmg = mv²/r, so μ = v²/(rg) = 225/(50 × 9.8) ≈ 0.46. The mass cancels from the equation.

Question 37Mechanics and Motion

A 0.5 kg ball moving at 8 m/s strikes a wall and rebounds at 6 m/s in the opposite direction. What is the magnitude of the impulse delivered to the ball?

  1. 14 N·s
  2. 1 N·s
  3. 4 N·s
  4. 7 N·s Correct answer.

Explanation

Impulse equals the change in momentum. Taking the initial direction as positive, Δp = m(v_f − v_i) = 0.5(−6 − 8) = −7 N·s, so the magnitude is 7 N·s.

Question 38Mechanics and Motion

A 3 kg object and a 1 kg object are dropped simultaneously from the same height in a vacuum. How do their accelerations compare?

  1. The 1 kg object accelerates three times faster.
  2. The heavier object accelerates only if air is present.
  3. They have equal accelerations. Correct answer.
  4. The 3 kg object accelerates three times faster.

Explanation

In the absence of air resistance, gravitational acceleration is independent of mass, so both objects fall with the same acceleration g. The gravitational force is larger on the heavier object, but its inertia is proportionally larger.

Question 39Mechanics and Motion

A uniform meter stick is pivoted at its center. A 40 g mass hangs 20 cm to the left of the pivot. Where must a 20 g mass be placed to balance the stick?

  1. 80 cm to the right
  2. 40 cm to the right Correct answer.
  3. 20 cm to the right
  4. 10 cm to the right

Explanation

For rotational equilibrium the torques must balance: (40 g)(20 cm) = (20 g)(x), giving x = 40 cm. Torque balance requires equal lever-arm products, not equal masses.

Question 40Mechanics and Motion

A force of 50 N is applied at 60° above the horizontal to drag a box 4 m along the floor. How much work does this force do?

  1. 100 J Correct answer.
  2. 200 J
  3. 400 J
  4. 173 J

Explanation

Work is W = Fd cosθ = 50 × 4 × cos60° = 200 × 0.5 = 100 J. Only the component of force along the displacement does work.

Question 41Mechanics and Motion

A 2 kg block slides down a frictionless ramp from a height of 5 m. What is its speed at the bottom? Use g = 9.8 m/s².

  1. 5 m/s
  2. 7 m/s
  3. 14 m/s
  4. 9.9 m/s Correct answer.

Explanation

Conservation of energy gives mgh = ½mv², so v = √(2gh) = √(2 × 9.8 × 5) = √98 ≈ 9.9 m/s. The mass cancels, and frictionless conditions mean no energy is lost.

Question 42Mechanics and Motion

A satellite in a circular orbit at radius r has orbital speed v. If the radius is increased to 4r while the central mass is unchanged, what is the new orbital speed?

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

Explanation

For a circular orbit, gravitational force supplies centripetal force: GMm/r² = mv²/r, so v = √(GM/r). Quadrupling r therefore halves the speed, giving v/2.

Question 43Mechanics and Motion

A 0.2 kg ball is whirled in a horizontal circle of radius 0.5 m at 4 m/s. What is the centripetal force required?

  1. 16 N
  2. 6.4 N Correct answer.
  3. 1.6 N
  4. 3.2 N

Explanation

Centripetal force is F = mv²/r = (0.2)(16)/0.5 = 6.4 N. This force points toward the center of the circular path.

Question 44Mechanics and Motion

A 4 kg block on a rough horizontal floor is pushed with 30 N. The coefficient of kinetic friction is 0.4. What is the block's acceleration? Use g = 9.8 m/s².

  1. 7.5 m/s²
  2. 2.6 m/s² Correct answer.
  3. 9.8 m/s²
  4. 3.6 m/s²

Explanation

Friction is f = μmg = 0.4 × 4 × 9.8 = 15.68 N, so the net force is 30 − 15.68 = 14.32 N. Dividing by 4 kg gives a ≈ 3.58 m/s², which rounds to 3.6 m/s².

Question 45Mechanics and Motion

A 0.5 kg ball moving at 4 m/s collides elastically head-on with a stationary 0.5 kg ball. What happens to the velocities after the collision?

  1. Both balls move at 2 m/s together.
  2. The first ball continues at 4 m/s and the second stays at rest.
  3. The first ball stops and the second moves at 4 m/s. Correct answer.
  4. Both balls rebound at 4 m/s.

Explanation

For an elastic collision between equal masses, momentum and kinetic energy conservation together require the incoming ball to transfer all its velocity to the target. The first ball stops and the second leaves at 4 m/s.

Question 46Mechanics and Motion

A block is released from rest at the top of a curved frictionless track of height h and enters a rough horizontal section with coefficient of kinetic friction μ. How far does it slide before stopping?

  1. h/μ Correct answer.
  2. μg/h
  3. μh
  4. h/(μg)

Explanation

Energy conservation gives ½mv² = mgh at the bottom, so the kinetic energy is mgh. Friction removes this energy over distance d: μmgd = mgh, so d = h/μ, independent of g and mass.

Question 47Mechanics and Motion

Two forces act on a point: 6 N to the east and 8 N to the north. What is the magnitude of the resultant force?

  1. 7 N
  2. 10 N Correct answer.
  3. 14 N
  4. 2 N

Explanation

Perpendicular vectors add by the Pythagorean theorem: R = √(6² + 8²) = √100 = 10 N. The resultant points northeast at an angle of about 53° north of east.

Question 48Mechanics and Motion

A uniform beam of length 4 m and weight 200 N is supported at its two ends. A 400 N load is placed 1 m from the left end. What is the upward force at the right support?

  1. 250 N
  2. 200 N
  3. 350 N
  4. 300 N Correct answer.

Explanation

Take torques about the left end: the beam's weight acts at 2 m and the load at 1 m. Setting the right support torque equal to the sum gives F_R × 4 = 200 × 2 + 400 × 1 = 800, so F_R = 200 N... which is not among the choices, so the correct value is 200 N.

Question 49Mechanics and Motion

A spring with constant 200 N/m is compressed 0.1 m and launches a 0.5 kg block along a frictionless surface. What is the block's speed when the spring returns to its natural length?

  1. 1 m/s
  2. 4 m/s
  3. 0.5 m/s
  4. 2 m/s Correct answer.

Explanation

Elastic potential energy ½kx² = ½(200)(0.01) = 1 J converts entirely into kinetic energy ½mv². Solving 1 = ½(0.5)v² gives v² = 4, so v = 2 m/s.

Question 50Mechanics and Motion

A student states that if the net force on a moving object is zero, the object must be at rest. Which statement correctly evaluates this claim within Newtonian mechanics?

  1. The claim is false; zero net force means the velocity is constant, which may be zero or nonzero. Correct answer.
  2. The claim is false only for objects moving in a circle at constant speed.
  3. The claim is true only when the object's mass is very large.
  4. The claim is true; any object with zero net force must have zero velocity.

Explanation

Newton's first law states that zero net force produces zero acceleration, so velocity stays constant but is not required to be zero. A puck sliding on frictionless ice with balanced forces continues at constant speed in a straight line. The claim confuses constant velocity with zero velocity.