OCR Further Mechanics AS 2019 June — Question 1

Exam BoardOCR
ModuleFurther Mechanics AS (Further Mechanics AS)
Year2019
SessionJune
TopicWork, energy and Power 2

1
\includegraphics[max width=\textwidth, alt={}, center]{74bada9e-60cf-4ed4-abd0-4be155b7cf81-2_533_424_402_246} A smooth wire is shaped into a circle of radius 2.5 m which is fixed in a vertical plane with its centre at a point \(O\). A small bead \(B\) is threaded onto the wire. \(B\) is held with \(O B\) vertical and is then projected horizontally with an initial speed of \(8.4 \mathrm {~ms} ^ { - 1 }\) (see diagram).
  1. Find the speed of \(B\) at the instant when \(O B\) makes an angle of 0.8 radians with the downward vertical through \(O\).
  2. Determine whether \(B\) has sufficient energy to reach the point on the wire vertically above \(O\).