Final answer:
The upward force Barry's finger tips must exert to keep the tray level is 23.8 N. He can ease the carrying by moving the plate of food closer to his thumb, which acts as the fulcrum.
Step-by-step explanation:
To determine the upward force that Barry's finger tips must exert to keep the tray level, we will use the principle of torques being balanced in rotational equilibrium. The torques about the fulcrum (thumb) due to the weight of the tray and the plate of food must be balanced by the torque due to the force exerted by the finger tips.
The torque (τ) is the product of the force (F) applied and the lever arm (r), the perpendicular distance from the axis of rotation to the line of action of the force: τ = F × r.
For the tray, the torque due to gravity on the tray is (0.20 kg × 9.8 m/s² × 0.25 m) because the center of gravity is at the middle of the tray. For the plate of food, the torque is (0.40 kg × 9.8 m/s² × 0.30 m). The sum of these torques must equal the torque provided by the fingers: (0.40 kg × 9.8 m/s² × 0.30 m) + (0.20 kg × 9.8 m/s² × 0.25 m) = F × 0.10 m, where F is the force exerted by the fingertips.
To solve for F, we divide the sum of the torques by the lever arm of the finger force (0.10 m).
Using the above calculations, the required upward force that Barry's finger tips must exert to keep the tray level is 23.8 N. The torque due to the weight of the tray and food is the combined mass times gravity times their respective distances from the right edge (lever arms).
For part b), Barry could make the tray easier to carry by balancing the weight closer to the fulcrum (his thumb). By moving the plate closer to the left edge, the required lifting force would decrease, making it less strenuous to hold the tray level.