ip a 9.00-g bullet, moving horizontally with an initial speed $v_0$, embeds itself in a 1.40-kg pendulum bob that is initially at rest. the length of the pendulum is $l = 0.750\text{ m}$. after the collision, the pendulum swings to one side and comes to rest when it has gained a vertical height of 14.0 cm.

part d
how long does it take for the bullet-bob system to come to rest for the first time?
$t =$ s

Question

ip a 9.00-g bullet, moving horizontally with an initial speed \$v_0\$, embeds itself in a 1.40-kg pendulum bob that is initially at rest. the length of the pendulum is \$l = 0.750\text{ m}\$. after the collision, the pendulum swings to one side and comes to rest when it has gained a vertical height of 14.0 cm.

part d
how long does it take for the bullet-bob system to come to rest for the first time?
\$t =\$ s

part d
how long does it take for the bullet-bob system to come to rest for the first time?
$t =$   s

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Ballistic Pendulum", "Simple Pendulum Period" ], "new_concepts": [], "current_concepts": [ "Ballistic Pendulum", "Simple Pendulum Period" ] } ## Identify the physical system and parameters $$ \begin{aligned} m &= 9.00\text{ g} = 0.00900\text{ kg} \ M &= 1.40\text{ kg} \ L &= 0.750\text{ m} \ h &= 14.0\text{ cm} = 0.140\text{ m} \ g &= 9.81\text{ m/s}^2 \end{aligned} $$ ## Relate the motion to simple harmonic motion $$ \begin{aligned} T &= 2\pi \sqrt{\frac{L}{g}} \ t &= \frac{T}{4} = \frac{\pi}{2} \sqrt{\frac{L}{g}} \end{aligned} $$ ## Calculate the time to come to rest $$ \begin{aligned} t &= \frac{\pi}{2} \sqrt{\frac{0.750}{9.81}} \ t &\approx 1.5708 \times 0.2766 \approx 0.435\text{ s} \end{aligned} $$ How long does it take for the bullet-bob system to come to rest for the first time? $t =$ $0.435$ $\text{s}$ { "subject": "Natural Science", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Natural Science", "Physics", "Simple Pendulum Period" ] }

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Question

Explanation:

Identify the physical system and parameters

Relate the motion to simple harmonic motion

Calculate the time to come to rest

Answer: