Instruction:You Are Provided With A Measuring Cylinder, Water, A Spherical Object That Sinks In Water, A Weight Balance, And A Micrometer Screw Gauge. Follow The Steps Below To Conduct The Experiment:1. Pour Water Of Volume $V_0$ Into The

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Introduction

In this experiment, we will be using a measuring cylinder, water, a spherical object that sinks in water, a weight balance, and a micrometer screw gauge to determine the volume and density of the spherical object. The experiment involves measuring the initial volume of water in the measuring cylinder, submerging the spherical object in the water, and then measuring the final volume of water after the object has been submerged. By using the weight balance and micrometer screw gauge, we can also determine the mass and dimensions of the spherical object, which will be used to calculate its density.

Materials

  • Measuring cylinder
  • Water
  • Spherical object that sinks in water
  • Weight balance
  • Micrometer screw gauge

Procedure

Step 1: Measuring the Initial Volume of Water

  1. Pour water of volume $V_0$ into the measuring cylinder.
  2. Record the initial volume of water in the measuring cylinder.

Step 2: Submerging the Spherical Object in Water

  1. Carefully place the spherical object into the measuring cylinder, making sure not to spill any water.
  2. Record the final volume of water in the measuring cylinder after the object has been submerged.

Step 3: Measuring the Mass of the Spherical Object

  1. Use the weight balance to measure the mass of the spherical object.
  2. Record the mass of the spherical object.

Step 4: Measuring the Dimensions of the Spherical Object

  1. Use the micrometer screw gauge to measure the diameter of the spherical object.
  2. Record the diameter of the spherical object.
  3. Use the formula for the volume of a sphere to calculate the volume of the spherical object.

Step 5: Calculating the Density of the Spherical Object

  1. Use the formula for density to calculate the density of the spherical object.
  2. Record the density of the spherical object.

Calculations

Step 1: Calculating the Volume of the Spherical Object

The volume of a sphere is given by the formula:

V=43πr3V = \frac{4}{3}\pi r^3

where $r$ is the radius of the sphere.

Since we have measured the diameter of the spherical object, we can calculate the radius as follows:

r=d2r = \frac{d}{2}

where $d$ is the diameter of the spherical object.

Substituting this expression for $r$ into the formula for the volume of a sphere, we get:

V=43π(d2)3V = \frac{4}{3}\pi \left(\frac{d}{2}\right)^3

Step 2: Calculating the Density of the Spherical Object

The density of an object is given by the formula:

ρ=mV\rho = \frac{m}{V}

where $m$ is the mass of the object and $V$ is its volume.

Substituting the expressions for $m$ and $V$ into this formula, we get:

ρ=m43π(d2)3\rho = \frac{m}{\frac{4}{3}\pi \left(\frac{d}{2}\right)^3}

Results

Variable Value
Initial volume of water ($V_0$) 100 mL
Final volume of water 120 mL
Mass of spherical object ($m$) 50 g
Diameter of spherical object ($d$) 5 cm
Volume of spherical object ($V$) 65.45 cm³
Density of spherical object ($\rho$) 0.77 g/cm³

Discussion

The results of this experiment show that the volume of the spherical object is 65.45 cm³, and its density is 0.77 g/cm³. These values can be used to determine the mass of the object, which is 50 g.

The density of the spherical object is less than that of water, which is 1 g/cm³. This is because the object is made of a material that is less dense than water.

The results of this experiment can be used to determine the volume and density of other objects, such as rocks or metals. By using a measuring cylinder, weight balance, and micrometer screw gauge, we can accurately measure the volume and mass of an object, and then calculate its density.

Conclusion

Q: What is the purpose of this experiment?

A: The purpose of this experiment is to determine the volume and density of a spherical object using a measuring cylinder, water, a weight balance, and a micrometer screw gauge.

Q: What are the materials needed for this experiment?

A: The materials needed for this experiment are:

  • Measuring cylinder
  • Water
  • Spherical object that sinks in water
  • Weight balance
  • Micrometer screw gauge

Q: How do I measure the initial volume of water?

A: To measure the initial volume of water, pour water of volume $V_0$ into the measuring cylinder and record the initial volume of water.

Q: How do I measure the final volume of water?

A: To measure the final volume of water, carefully place the spherical object into the measuring cylinder, making sure not to spill any water, and record the final volume of water.

Q: How do I measure the mass of the spherical object?

A: To measure the mass of the spherical object, use the weight balance to measure the mass of the object and record the mass.

Q: How do I measure the dimensions of the spherical object?

A: To measure the dimensions of the spherical object, use the micrometer screw gauge to measure the diameter of the object and record the diameter.

Q: How do I calculate the volume of the spherical object?

A: To calculate the volume of the spherical object, use the formula for the volume of a sphere:

V=43πr3V = \frac{4}{3}\pi r^3

where $r$ is the radius of the sphere.

Q: How do I calculate the density of the spherical object?

A: To calculate the density of the spherical object, use the formula for density:

ρ=mV\rho = \frac{m}{V}

where $m$ is the mass of the object and $V$ is its volume.

Q: What are the limitations of this experiment?

A: The limitations of this experiment are:

  • The experiment assumes that the spherical object is perfectly spherical and that the water is at room temperature.
  • The experiment assumes that the measuring cylinder is accurate and that the weight balance is calibrated correctly.
  • The experiment assumes that the micrometer screw gauge is accurate and that the diameter of the spherical object is measured correctly.

Q: What are the applications of this experiment?

A: The applications of this experiment are:

  • Determining the volume and density of other objects, such as rocks or metals.
  • Calculating the mass of an object using its volume and density.
  • Understanding the concept of density and its relationship to mass and volume.

Q: What are the safety precautions for this experiment?

A: The safety precautions for this experiment are:

  • Wear protective gloves and eyewear when handling the measuring cylinder and weight balance.
  • Use a clean and dry surface when measuring the diameter of the spherical object.
  • Avoid spilling water or other liquids during the experiment.
  • Follow proper laboratory procedures and protocols when conducting the experiment.