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Edexcel IAL Mathematics M2.3 work and energy

Practise M2 work and energy by linking kinetic energy, gravitational potential energy, resistance, friction and power in particle or vehicle models.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • Build a work-energy equation with KE change, GPE change and work against friction or resistance.
  • Use P=Fv or conservation of mechanical energy to find speed, acceleration or total work done.

Covered syllabus points

M2.3.1 - Kinetic and potential energy, work

M2.3 - Work and energy question 1

[Maximum number: 3]
Figure 5

Figure 5

A thin smooth hollow spherical shell has centre O and radius r. Part of the shell is removed to form a bowl with a plane circular rim. The bowl is fixed with the circular rim uppermost and horizontal. The point A is the lowest point of the bowl, as shown in Figure 5.

The point B is on the rim of the bowl, with OB at an angle θ\theta to the upward vertical, where tan⁡θ=125\tan \theta=\frac{12}{5}
A small ball is placed in the bowl at A. The ball is projected from A with horizontal speed u and moves in the vertical plane AOB. The ball stays in contact with the bowl until it reaches B.

At the instant when the ball reaches B, the speed of the ball is v.
By modelling the ball as a particle and ignoring air resistance,

use the principle of conservation of mechanical energy to show that

v2=u2−3613grv^{2}=u^{2}-\frac{36}{13} g r
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