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MMLU-Pro / 9135 / An automobile with a mass of 1000 mathrm{~kg}, including passengers, settles…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

An automobile with a mass of $1000 \mathrm{~kg}$, including passengers, settles $1.0 \mathrm{~cm}$ closer to the road for every additional $100 \mathrm{~kg}$ of passengers. It is driven with a constant horizontal component of speed $20 \mathrm{~km} / \mathrm{h}$ over a washboard road with sinusoidal bumps. The amplitude and wavelength of the sine curve are $5.0 \mathrm{~cm}$ and $20 \mathrm{~cm}$, respectively. The distance between the front and back wheels is $2.4 \mathrm{~m}$. Find the amplitude of oscillation of the automobile, assuming it moves vertically as an undamped driven harmonic oscillator. Neglect the mass of the wheels and springs and assume that the wheels are always in contact with the road.
Plain-text mathematical notation (without MathML)
 An automobile with a mass of $1000 \mathrm{~kg}$, including passengers, settles $1.0 \mathrm{~cm}$ closer to the road for every additional $100 \mathrm{~kg}$ of passengers. It is driven with a constant horizontal component of speed $20 \mathrm{~km} / \mathrm{h}$ over a washboard road with sinusoidal bumps. The amplitude and wavelength of the sine curve are $5.0 \mathrm{~cm}$ and $20 \mathrm{~cm}$, respectively. The distance between the front and back wheels is $2.4 \mathrm{~m}$. Find the amplitude of oscillation of the automobile, assuming it moves vertically as an undamped driven harmonic oscillator. Neglect the mass of the wheels and springs and assume that the wheels are always in contact with the road.
Original LaTeX notation
 An automobile with a mass of $1000 \mathrm{~kg}$, including passengers, settles $1.0 \mathrm{~cm}$ closer to the road for every additional $100 \mathrm{~kg}$ of passengers. It is driven with a constant horizontal component of speed $20 \mathrm{~km} / \mathrm{h}$ over a washboard road with sinusoidal bumps. The amplitude and wavelength of the sine curve are $5.0 \mathrm{~cm}$ and $20 \mathrm{~cm}$, respectively. The distance between the front and back wheels is $2.4 \mathrm{~m}$. Find the amplitude of oscillation of the automobile, assuming it moves vertically as an undamped driven harmonic oscillator. Neglect the mass of the wheels and springs and assume that the wheels are always in contact with the road.

category

physics

options

  1. -0.1 $ \mathrm{~mm}$
  2. -0.3 $\mathrm{~mm}$
  3. 0.05 $ \mathrm{~mm}$
  4. 0.25 $\mathrm{~mm}$
  5. -0.16 $ \mathrm{~mm}$
  6. -0.25 $\mathrm{~mm}$
  7. 0.2 $ \mathrm{~mm}$
  8. 1.0 $\mathrm{~mm}$
  9. 0.1 $\mathrm{~mm}$
  10. -0.5 $\mathrm{~mm}$

src

scibench-class

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Source and history

upstream_id / Original problem ID
9135
task_id
43d63a17-2cec-56e4-8508-8d78bd8d56b6
task_key
default--test--9135
task_revision_id
1
config / split
default / test

Official source

initial import