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Ch 15: Oscillations

Knight Calc - Physics for Scientists and Engineers 5th Edition

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

모든 교과서

Knight Calc 5th Edition

Ch 15: Oscillations

문제 41a

15장, 문제 41a

When the displacement of a mass on a spring is (½)A, what fraction of the energy is kinetic energy and what fraction is potential energy?

검증된 단계별 안내

1

Start by recalling the total mechanical energy of a mass-spring system, which is the sum of kinetic energy (KE) and potential energy (PE). The total energy is given by:

E = U^{2} + K^{2}

, where

U

is potential energy and

K

kinetic energy

Recall the potential energy in a spring is given by:

U = 1/2 k^{2}

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

6m

주요 개념

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

Hooke's Law

Hooke's Law states that the force exerted by a spring is directly proportional to its displacement from the equilibrium position, expressed as F = -kx, where k is the spring constant. This principle is fundamental in understanding how springs store potential energy when displaced.

추천 영상:

가이드 코스

Spring Force (Hooke's Law)

Potential Energy in Springs

The potential energy (PE) stored in a spring is given by the formula PE = 1/2 kx², where x is the displacement from the equilibrium position. This energy is maximum when the spring is fully compressed or stretched and decreases as the spring returns to its equilibrium position.

추천 영상:

가이드 코스

Energy in Horizontal Springs

Kinetic Energy

Kinetic energy (KE) is the energy of an object due to its motion, calculated using the formula KE = 1/2 mv², where m is mass and v is velocity. In the context of a mass on a spring, kinetic energy is highest when the mass passes through the equilibrium position, where potential energy is zero.

추천 영상:

가이드 코스

Intro to Rotational Kinetic Energy

관련 실천

교과서 질문

An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk (m = 0.10 g) driven back and forth in SHM at 1.0 MHz by an electromagnetic coil. What is the disk's maximum speed at this amplitude?

교과서 질문

Vision is blurred if the head is vibrated at 29 Hz because the vibrations are resonant with the natural frequency of the eyeball in its socket. If the mass of the eyeball is 7.5 g, a typical value, what is the effective spring constant of the musculature that holds the eyeball in the socket?

교과서 질문

Astronauts in space cannot weigh themselves by standing on a bathroom scale. Instead, they determine their mass by oscillating on a large spring. Suppose an astronaut attaches one end of a large spring to her belt and the other end to a hook on the wall of the space capsule. A fellow astronaut then pulls her away from the wall and releases her. The spring's length as a function of time is shown in FIGURE P15.46. What is her speed when the spring's length is 1.2 m?

교과서 질문

A 350 g mass on a 45-cm-long string is released at an angle of 4.5° from vertical. It has a damping constant of 0.010 kg/s. After 25 s, (a) how many oscillations has it completed and (b) what fraction of the initial energy has been lost?

교과서 질문

A 100 g block attached to a spring with spring constant 2.5 N/m oscillates horizontally on a frictionless table. Its velocity is 20 c/m when 𝓍 = -5.0 cm What is the block's position when the acceleration is maximum?

교과서 질문

Two 500 g air-track gliders are each connected by identical springs with spring constant 25 N/m to the ends of the air track. The gliders are connected to each other by a spring with spring constant 2.0 N/m. One glider is pulled 8.0 cm to the side and released while the other is at rest at its equilibrium position. How long will it take until the glider that was initially at rest has all the motion while the first glider is at rest?