1st Step for All

Science: 천문학 Astronomy; 생물학 Biology; 화학 Chemistry; 지질학 Geology; 수학 Mathematics; 물리 Physics

Engineering: 항공우주 Aerospace; 농업 Agriculture; 생물 Biological; 화학 Chemical; 토목공학 Civil; 전기공학 Electrical; 환경 Environmental; 산업 Industrial; 해양 Marine; 재료 Materials; 기계 Mechanical; 원자력 Nuclear

Architecture: 건축 Architecture

Health: 건강보건 Health

ETC: 기타 ETC

현재 위치

Velocity when the slid object escapes from the hemisphere surface

작성자 Uploader : corona 작성일 Upload Date: 2019-09-23변경일 Update Date: 2020-03-14조회수 View : 254

As shown in the figure, the object at the apex of the hemisphere with a radius of R (m) starts to slide. The velocity V (m/s) at the moment of departure when the obhect escapes from the hemisphere surface by acceleration is obtained as follows.

It is assumed that there is no friction between the hemisphere and the object.

The velocity V of the object at the position, where the line connecting the center of the hemisphere and the object is angled at θ with respect to the horizontal line, is as follows.

V = (2*g*R*(1-sinθ))^(1/2)

If the mass of the object is m, the centrifugal force F1 at this time is as follows.

F1 = m*V^2/R = m*2*g*R*(1-sinθ)/R = 2*m*g*(1-sinθ)

On the other hand, the centripetal force F2 toward the center of the sphere due to gravity is as follows.

F2 = m*g*sinθ

At the moment F1 = F2, it starts to deviate from the surface of the hemisphere. Then,

2*m*g*(1-sinθ) = m*g*sinθ

sinθ = 2/3

Therefore, the velocity V is as follows.

V = (2*g*R/3)^(1/2)

*** 참고문헌[References] ***

V = (2*g*R/3)^(1/2)

작성자의 수식그림이 없습니다. No picture for this formula


변수명 Variable	변수값 Value	변 수 설 명 Description of the variable

※ 이 사이트는 광고수익으로 운영됩니다.

★ 로그인 후 수식작성 및 즐겨찾기에 추가할 수 있습니다.
★ To make new formula or to add this formula in your bookmark, log on please.

1st Step for All

현재 위치

Velocity when the slid object escapes from the hemisphere surface

코멘트