Ch 08: Dynamics II: Motion in a Plane

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

Knight Calc 5th Edition

Ch 08: Dynamics II: Motion in a Plane

문제 8a

8장, 문제 8a

A 200 g block on a 50-cm-long string swings in a circle on a horizontal, frictionless table at 75 rpm. What is the speed of the block?

검증된 단계별 안내

Convert the given mass of the block from grams to kilograms. Since 1 g = 0.001 kg, the mass of the block is \( m = 200 \times 0.001 \; \text{kg} \).

Convert the length of the string from centimeters to meters. Since 1 cm = 0.01 m, the length of the string is \( r = 50 \times 0.01 \; \text{m} \).

Convert the rotational speed from revolutions per minute (rpm) to angular velocity in radians per second. Use the formula \( \omega = \frac{2 \pi \; \text{rad}}{1 \; \text{rev}} \times \frac{75 \; \text{rev}}{60 \; \text{s}} \).

Relate the linear speed \( v \) of the block to the angular velocity \( \omega \) using the formula \( v = r \omega \), where \( r \) is the radius of the circular motion (equal to the length of the string).

Substitute the values of \( r \) and \( \omega \) into the formula \( v = r \omega \) to calculate the speed of the block.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Centripetal Force

Centripetal force is the net force acting on an object moving in a circular path, directed towards the center of the circle. It is essential for maintaining circular motion and is provided by tension, gravity, or friction, depending on the scenario. In this case, the tension in the string provides the necessary centripetal force to keep the block moving in a circle.

Linear Speed

Linear speed refers to the distance traveled by an object per unit of time. For an object moving in a circle, the linear speed can be calculated using the formula v = 2πr/T, where r is the radius of the circle and T is the period of rotation. In this problem, the speed of the block can be derived from its rotational speed in revolutions per minute (rpm) and the radius of the circular path.

Conversion of Units

Conversion of units is a critical skill in physics that involves changing a measurement from one unit to another to facilitate calculations. In this question, converting the block's rotational speed from revolutions per minute (rpm) to a linear speed in meters per second (m/s) is necessary for solving the problem. Understanding how to convert between different units ensures accurate results in calculations involving speed and distance.

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