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ENGR5004 / Week 8
ENGR216 2017 Q B1Past paperOld spec ENGR2162:125 marks30 min

ENGR216 Summer 2017 Q B1[VALID] official answers

Answer ALL parts (a) - (c)

The storage cupboard shown in Figure B1 has a mass of 30 kg and contacts the floor via rollers at the points shown. The location of the centre of gravity (G) and the point of application of an externally applied force (200 N) are also shown in the Figure.

Figure B1: storage cupboard on two floor rollers 0.9 m apart; centre of gravity G midway between the rollers, 1.2 m above the floor; a horizontal 200 N force pushes on the left face at height h above the floor.
Figure B1: storage cupboard on two floor rollers 0.9 m apart; centre of gravity G midway between the rollers, 1.2 m above the floor; a horizontal 200 N force pushes on the left face at height h above the floor.
Formulas you may need
  • Force equation for the mass centre: ∑F=maG\sum \mathbf{F} = m\mathbf{a}_G (given in the 2017 Section B formula sheet; not on the 2026 sheet, so learn this)
  • Rigid-body translation: α=0\alpha = 0, so ∑MG=0\sum M_G = 0, or about any point P, ∑MP=(maG) d\sum M_P = (m a_G)\,d where dd is the moment arm of maGm\mathbf{a}_G about P (learn this)
  • Kinetic (sliding) friction F=μNF = \mu N, opposing the sliding motion (learn this)
  • Tipping condition: a roller is about to lift when its normal reaction falls to zero (learn this)
  1. (a)
    For the loading condition shown in Figure B1, draw free body and kinetic diagrams of the cabinet, making the assumption that there is no friction acting between the floor and the rollers. Calculate the acceleration of the cupboard when acted on by the 200 N force.
    [8]Third
  2. (b)
    If there is no friction between the floor and the rollers, calculate the values of dimension h for which the cupboard is not predicted to tip over when acted on by the 200 N force.
    [9]
  3. (c)
    If the rollers are locked into position such that the coefficient of sliding friction between the rollers and the floor takes a value of μ=0.3\mu = 0.3, determine the acceleration of the cupboard when acted on by the 200 N force.
    [8]2:2