Final answer:
To find the density of an object suspended from a spring balance, subtract the reading in water from the reading in air to find the buoyant force. Then, calculate the volume of water displaced, which is equal to the volume of the object. Finally, divide the weight of the object in air by this volume to find the object's density.
Step-by-step explanation:
When an object is suspended from a spring balance and the reading is 8.40 N, this represents the actual weight of the object in air. When the same object is fully submerged in water and the reading on the spring balance is 7.20 N, this lower reading is due to the buoyant force exerted by the water on the object. To determine the density of the object, we can use the principle of buoyancy as described by Archimedes' principle.
The apparent weight loss of the object when submerged in water (which is 8.40 N - 7.20 N = 1.20 N) is equal to the buoyant force, which in turn is equal to the weight of the water displaced by the object. Using the formula for buoyant force, F_b = V ⋅ ρ_w ⋅ g, where F_b is the buoyant force, V is the volume of the object (and thus the volume of water displaced), ρ_w is the density of water (approximately 1000 kg/m³), and g is the acceleration due to gravity (approximately 9.81 m/s²). By rearranging for V, we find the volume displaced. We can then calculate the density of the object (ρ_object) by dividing the object's weight in air by the volume of water displaced (ρ_object = weight_in_air / V).