WAEC Further Mathematics 2016 Paper

Concept:When a lift accelerates upwards, the floor reaction must balance the man’s weight and also provide the extra upward force needed for acceleration.Explanation:Let the reaction from the floor of the lift be $R$.Take the upward direction as positive.Downward force on the man is his weight: $mg$.Upward force on the man is the floor reaction: $R$.The net upward force is therefore $R - mg$.By Newton’s second law, this net force equals $ma$.So, $R - mg = ma$.Rearrange the equation: $R = mg + ma$.Given $m = 80\;\mathrm{kg}$, $g = 10\;\mathrm{m\,s^{-2}}$, and $a = 0.5\;\mathrm{m\,s^{-2}}$:$R = (80 \times 10) + (80 \times 0.5)$$R = 800 + 40$$R = 840\;\mathrm{N}$Thus, the floor of the lift pushes upward on the man with a reaction of $840\;\mathrm{N}$.Answer:$840\;\mathrm{N}$ $\;$ (Option D).