two people with a combined mass of 126 kg hop into an old car with worn-out shock absorbers. this causes the springs to compress by 9.80 cm. when the car hits a bump in the road, it oscillates up and down with a period of 1.77 s.

part a
find the total load supported by the springs.
$m + m =$ kg

part b
find the mass of the car.
$m =$ kg

Question

two people with a combined mass of 126 kg hop into an old car with worn-out shock absorbers. this causes the springs to compress by 9.80 cm. when the car hits a bump in the road, it oscillates up and down with a period of 1.77 s.

part a
find the total load supported by the springs.
\$m + m =\$ kg

part b
find the mass of the car.
\$m =\$ kg

part a
find the total load supported by the springs.
$m + m =$   kg

part b
find the mass of the car.
$m =$   kg

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Spring Constant Calculation", "Simple Harmonic Motion Period" ], "new_concepts": [], "current_concepts": [ "Spring Constant Calculation", "Simple Harmonic Motion Period" ] } ## Calculate the spring constant of the suspension Using the *Spring Constant Calculation* knowledge point $$ \begin{aligned} k &= \frac{m_{\text{people}} g}{x} \ k &= \frac{126 \text{ kg} \times 9.80 \text{ m/s}^2}{0.0980 \text{ m}} = 12600 \text{ N/m} \end{aligned} $$ ## Calculate the total load supported by the springs Using the *Simple Harmonic Motion Period* knowledge point $$ \begin{aligned} T &= 2\pi \sqrt{\frac{M + m}{k}} \ M + m &= \frac{k T^2}{4\pi^2} \ M + m &= \frac{12600 \text{ N/m} \times (1.77 \text{ s})^2}{4\pi^2} \approx 999.56 \text{ kg} \approx 1.00 \times 10^3 \text{ kg} \end{aligned} $$ ## Calculate the mass of the car Using the *Simple Harmonic Motion Period* knowledge point $$ \begin{aligned} M &= (M + m) - m_{\text{people}} \ M &= 999.56 \text{ kg} - 126 \text{ kg} = 873.56 \text{ kg} \approx 874 \text{ kg} \end{aligned} $$ ## Question 1 $1.00 \times 10^3$ ## Question 2 $874$ { "subject": "Natural Science", "question_type": "Multi-part", "knowledge_point": [ "Natural Science", "Physics", "Simple Harmonic Motion" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the spring constant of the suspension

Calculate the total load supported by the springs

Calculate the mass of the car

Answer:

Question 1

Question 2