A 1.00-kg beaker containing 2.0 kg of oil (density = 916 kg/m3) rests on a scale. A 2.00-kg block of iron is suspended from a spring scale and is completely submerged in the oil. Find the equilibrium readings of both scales.

I was able to find the equilibrium reading for the spring scale but not the scale the beaker is resting on. Can you please explain what forces are used to find this answer as well. Thank You!

What do you get for the spring scale?

The weight of liquid displaced should be the difference in each scale if they had been weighed separately.

2pi+72apples

17.4

To find the equilibrium reading on the scale that the beaker is resting on, we need to consider the forces acting on the system.

Let's break it down step by step:

1. The beaker and its contents create a downward force due to their combined weight. The weight is given by the formula: weight = mass × gravity. In this case, the weight of the beaker (1.00 kg) and the weight of the oil (2.0 kg) need to be considered separately.

Weight of the beaker: beaker_weight = 1.00 kg × 9.8 m/s^2 (acceleration due to gravity)
Weight of the oil: oil_weight = oil_mass × 9.8 m/s^2

2. The upward force acting on the system is the buoyant force. When an object is submerged in a fluid, it experiences an upward force called the buoyant force, which is equal to the weight of the displaced fluid. The buoyant force can be calculated using the formula: buoyant_force = fluid_density × fluid_volume × gravity.

For the iron block submerged in oil, the buoyant force can be calculated as follows:
buoyant_force = oil_density × iron_volume × gravity

3. Finally, to find the equilibrium reading on the scale that the beaker is resting on, we subtract the buoyant force from the weight of the beaker and oil.

equilibrium_reading = (beaker_weight + oil_weight) - buoyant_force

Now, let's put it all together with the given values:

- Beaker weight: 1.00 kg × 9.8 m/s^2 = 9.8 N
- Oil weight: 2.0 kg × 9.8 m/s^2 = 19.6 N

To calculate the buoyant force, we need the volume of the iron block. Since the density of iron is approximately 7,860 kg/m3, we can use the relationship:

iron_mass = iron_density × iron_volume

Solving for volume gives:

iron_volume = iron_mass / iron_density
iron_volume = 2.00 kg / 7,860 kg/m3
iron_volume = 0.000254 m3

Now let's calculate the buoyant force:

buoyant_force = oil_density × iron_volume × gravity
buoyant_force = 916 kg/m3 × 0.000254 m3 × 9.8 m/s^2
buoyant_force ≈ 2.25 N

Finally, the equilibrium reading on the scale that the beaker is resting on is given by:

equilibrium_reading = (beaker_weight + oil_weight) - buoyant_force
equilibrium_reading = (9.8 N + 19.6 N) - 2.25 N
equilibrium_reading ≈ 27.15 N

Thus, the equilibrium reading on the scale that the beaker is resting on is approximately 27.15 N.