a peg on a turntable moves with a constant tangential speed of $0.68\text{ m/s}$ in a circle of radius $0.25\text{ m}$. the peg casts a shadow on a wall. find the following quantities related to the motion of the shadow.

part d
find the maximum magnitude of the acceleration.
express your answer using two significant figures.
$a_{\text{max}} = $ $\text{m/s}^2$

Question

a peg on a turntable moves with a constant tangential speed of $0.68\text{ m/s}$ in a circle of radius $0.25\text{ m}$. the peg casts a shadow on a wall. find the following quantities related to the motion of the shadow.

part d
find the maximum magnitude of the acceleration.
express your answer using two significant figures.
$a_{\text{max}} = $ $\text{m/s}^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Shadow Motion Acceleration", "Uniform Circular Motion Period" ], "current_concepts": [ "Shadow Motion Acceleration", "Uniform Circular Motion Period" ] } ## Relate shadow acceleration to circular motion parameters $$ \begin{aligned} v &= 0.68\text{ m/s}\ r &= 0.25\text{ m} \end{aligned} $$ ## Calculate maximum acceleration magnitude $$ \begin{aligned} a_{\max} &= \frac{v^2}{r}\ a_{\max} &= \frac{(0.68)^2}{0.25}\ a_{\max} &= \frac{0.4624}{0.25}\ a_{\max} &= 1.8496\text{ m/s}^2 \end{aligned} $$ ## Round to two significant figures $$ a_{\max} \approx 1.8\text{ m/s}^2 $$ Find the maximum magnitude of the acceleration. Express your answer using two significant figures. $a_{\max} =$ 1.8 $\text{m/s}^2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Shadow Motion Acceleration" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Relate shadow acceleration to circular motion parameters

Calculate maximum acceleration magnitude

Round to two significant figures

Answer: