Final answer:
Hana must apply approximately 44 N of force to lift the other end of the 4.0 m plank, making the correct answer (a) 44 N.
Step-by-step explanation:
To determine the force Hana must apply to lift the other end of the plank, we need to use the concept of torque in physics. The torque (τ) due to the dog's weight about the axis of rotation (the end of the plank resting on the ground) is given by the product of the force due to the dog's weight and the perpendicular distance from the axis of rotation to the line of action of the force. The force due to the dog's weight (Fw) is the dog's mass (m) times gravitational acceleration (g), which is Fw = mg. Since the mass (m) is given as 18 kg and g is approximately 9.8 m/s2, Fw = 18 kg × 9.8 m/s2 = 176.4 N. The dog is sitting 1.0 m from the end, so the torque due to the dog's weight is τ = Fw × distance = 176.4 N × 1.0 m = 176.4 N·m. To lift the other end of the plank without acceleration, the torque applied by Hana must be equal and opposite to the torque due to the dog's weight. Assuming the plank to be massless, the force Hana needs to apply (Fh) at 4.0 m from the axis of rotation is such that the applied torque equals to the dog's torque. Therefore, τ = Fh × 4.0 m, and solving for Fh gives Fh = 176.4 N·m / 4.0 m = 44.1 N. Thus, Hana must apply approximately 44 N of force to lift the other end of the plank. Therefore, the answer is (a) 44 N.