How can you determine if a steel ball of known radius is hollow? List the equipment that you will need for the experiment, and describe the procedure and calculations. Can you determine how big the hollow part is if present in the ball?
To determine if a steel ball is hollow and calculate the size of the hollow part if present, you can use the following equipment and procedure:
Equipment:
1. Vernier caliper or micrometer - used to measure the radius of the steel ball.
2. Water container - a small container that can hold enough water to fully immerse the steel ball.
3. Measuring cylinder or graduated cylinder - used to measure the volume of water displaced.
Procedure:
1. Measure the radius (r) of the steel ball using a vernier caliper or micrometer. Ensure that the ball's surface is clean and dry before taking the measurement.
2. Fill the water container with enough water to fully submerge the steel ball.
3. Gently lower the steel ball into the water, ensuring that it is completely immersed. Take care not to introduce any air bubbles.
4. Measure the volume of water displaced by the steel ball. To do this:
a. Place a measuring cylinder or graduated cylinder below the water container to collect the displaced water.
b. Slowly lower the steel ball into the measuring cylinder, allowing the water to flow into the cylinder. Make sure no water spills.
c. Note the volume of water in the measuring cylinder. This represents the volume of the hollow part, if present, in the steel ball.
Calculations:
To determine if the steel ball is hollow:
- If the volume of water displaced is equal to the volume of a solid sphere with a radius r, then the steel ball is solid.
- If the volume of water displaced is less than the volume of a solid sphere with a radius r, then the steel ball is hollow.
To calculate the size of the hollow part (if present) in the steel ball:
1. Calculate the volume of a solid sphere using the formula: V = (4/3) * π * r^3, where V is the volume and r is the radius of the ball.
2. Subtract the volume of the water displaced from the calculated volume of the solid sphere:
Hollow Part Volume = Volume of Solid Sphere - Volume of Water Displaced
3. By knowing the hollow part volume, the size can be described in different terms, such as the volume of the hollow part or the thickness of the hollow shell.
Note: It is important to ensure accurate measurements and perform the experiment carefully to obtain reliable results.