A 1.00-kg beaker containing 2.29 kg of oil (density = 916 kg/m3) rests on a scale. A 2.33-kg block of iron is suspended from a spring scale and is completely submerged in the oil (see figure below). Find the equilibrium readings of both scales.

top scale
N

bottom scale
N

User Icon for Damon Damon answered
8 years ago

need density of iron

top scale has
2.33 - Viron*916
but Viron = 2.33/density of iron

User Icon for Explain Bot Explain Bot answered
11 months ago

To find the equilibrium readings of both scales, let's analyze the forces acting on the system.

1. The beaker containing the oil is resting on a scale. The weight of the beaker and the oil will be acting downwards. The equation to calculate the weight is:

Weight = mass * gravitational acceleration

Given that the mass of the beaker and oil is 1.00 kg + 2.29 kg = 3.29 kg, and the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the weight:

Weight of beaker and oil = 3.29 kg * 9.8 m/s^2 = 32.142 N

So, the top scale reading will be 32.142 N.

2. The iron block is completely submerged in the oil. It will experience a buoyant force upwards and its weight downwards. The net force on the iron block will be zero for it to be in equilibrium.

The buoyant force is given by:

Buoyant force = Volume of the submerged block * Density of the fluid * Gravitational acceleration

The volume of the submerged block can be calculated using its density and mass:

Volume of block = Mass of block / Density of iron

Given that the mass of the block is 2.33 kg and the density of iron is approximately 7,860 kg/m^3, we can calculate the volume:

Volume of block = 2.33 kg / 7,860 kg/m^3 ≈ 0.000296 m^3

Now we can calculate the buoyant force:

Buoyant force = 0.000296 m^3 * 916 kg/m^3 * 9.8 m/s^2 ≈ 2.7 N

So, the net force acting on the iron block will be its weight minus the buoyant force:

Net force on the block = Weight of block - Buoyant force

Weight of block = mass * gravitational acceleration

Weight of block = 2.33 kg * 9.8 m/s^2 ≈ 22.834 N

Net force on the block = 22.834 N - 2.7 N ≈ 20.134 N

Hence, the bottom scale reading will be approximately 20.134 N.

Therefore, the equilibrium readings of the scales are:

Top scale: 32.142 N
Bottom scale: 20.134 N