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The 50cm mark isn't necessarily the ruler's centre of mass where it will balance. If the ruler is not uniform (i.e. it has a hole in it) its centre of mass will not be exactly in the middle.
Metric ruler
meter stick
Finding the weight of a ruler using momentsApparatus:Metre ruler, knife edge, set of 100g masses [M20C]Diagram:Procedure:1. Place the metre ruler (without the weight shown in the above diagram) on the knife edge so that it is balanced.The knife edge should be roughly below the 50cm mark on the ruler. Note down the precise position of the knife edge below the ruler to the nearest mm. This is the position of the ruler's centre of gravity.2. Place a 100g mass, a weight of 1N, near the left-hand end of the ruler as shown in the diagram above.The ruler will tip down on this side.3. Move the knife edge towards the weight until the ruler again balances.Measure the distance p (in mm) between the centre of the weight and the new knife edge position and thedistance q (in mm) between the new knife edge position and the position of the centre of gravity of the ruler(see diagram above).4. Record your measurements in a table with the headings shown below.5. Repeat stages 2 to 4 for weights of 2N (using 200g of mass) to 9N (900g mass).Calculations:1. When the ruler is balanced the anticlockwise moment caused by the weight of the masses is equal to the clockwise moment caused by the weight of the ruler.Therefore:weight of mass, W (N) x distance p (mm) = ruler weight R (N) x distance q (mm)2. Calculate the value distance, q divided by weight of mass , W [q / W] for each of your results in the appropriate column in the table.Weight of mass Win newtonsDistance p(mm)Distance q(mm)q divided by W(mm/N)3. Draw a graph of distance p (mm) [Y-AXIS] against q / W (mm/N) [X-AXIS]4. Measure the gradient of this graph.The gradient is equal to the weight of the ruler in newtons.Write out clearly your answer.5. Explain why the gradient of your graph equals the weight of the ruler
A balance will give you it's mass.
The 50cm mark isn't necessarily the ruler's centre of mass where it will balance. If the ruler is not uniform (i.e. it has a hole in it) its centre of mass will not be exactly in the middle.
Metric ruler
Jizz
Take an elemental mass on the solid hemisphere. Let the mass be in thin form of discs. The centre of mass lies at the centre of the disc. Integrate the whole function to get the c.o.m.
meter stick
what is mass
draw a symetrical raindrop. draw the lines of symmetry on it then where the lines cross is where the centre of mass it is
mass=density/volume
You're pretty much up a creek. You can find the volume using only a ruler, but without a way to find the mass, you will not be able to determine the density.
Finding the weight of a ruler using momentsApparatus:Metre ruler, knife edge, set of 100g masses [M20C]Diagram:Procedure:1. Place the metre ruler (without the weight shown in the above diagram) on the knife edge so that it is balanced.The knife edge should be roughly below the 50cm mark on the ruler. Note down the precise position of the knife edge below the ruler to the nearest mm. This is the position of the ruler's centre of gravity.2. Place a 100g mass, a weight of 1N, near the left-hand end of the ruler as shown in the diagram above.The ruler will tip down on this side.3. Move the knife edge towards the weight until the ruler again balances.Measure the distance p (in mm) between the centre of the weight and the new knife edge position and thedistance q (in mm) between the new knife edge position and the position of the centre of gravity of the ruler(see diagram above).4. Record your measurements in a table with the headings shown below.5. Repeat stages 2 to 4 for weights of 2N (using 200g of mass) to 9N (900g mass).Calculations:1. When the ruler is balanced the anticlockwise moment caused by the weight of the masses is equal to the clockwise moment caused by the weight of the ruler.Therefore:weight of mass, W (N) x distance p (mm) = ruler weight R (N) x distance q (mm)2. Calculate the value distance, q divided by weight of mass , W [q / W] for each of your results in the appropriate column in the table.Weight of mass Win newtonsDistance p(mm)Distance q(mm)q divided by W(mm/N)3. Draw a graph of distance p (mm) [Y-AXIS] against q / W (mm/N) [X-AXIS]4. Measure the gradient of this graph.The gradient is equal to the weight of the ruler in newtons.Write out clearly your answer.5. Explain why the gradient of your graph equals the weight of the ruler
A balance will give you it's mass.
To find the density you need the mass and volume and then, density = mass/volume. Given a ruler, you can easily measure an edge of the cube. If that is x units, then the volume is x3 cubic units. However, it is not clear how you find a mass with just a balance. You need some standard weights, but these do not appear to be provided. You are stuck and cannot answer the question.