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Name: Brandon Sookdeo Date: 05/12/13 Title: Hooke’s Law Aim: 1. To determine the spring constant of a spring 2. To determine the density of water by immersing a mass suspended by a spring into a beaker of water. Materials & Apparatus:

50 cm rule Retort stands (2) Spring Pointer (2) Masses Mass holder Beaker Vernier callipers Water

Diagram 1:

Name: Brandon Sookdeo

Figure 1 showing setup of apparatus to determine the spring constant of a spring. Diagram 2:

Figure 2 showing the setup of apparatus to determine the density of water.

Name: Brandon Sookdeo Theory: Hooke’s law states the up to some maximum load (known as the limit of proportionality) the extension of a wire or spring is proportional to the applied load. Hooke's law can be written as: F = ke Where F = force applied to the spring k is the spring constant e is extension = new length - original length There are two different types of deformation 1. Elastic deformation where the material returns to its original length when the force applied is removed. 2. Plastic deformation where the material retains some of the extension even after the force is removed. By plotting a force extension graph (F vs e) and finding the gradient of the line produced one can find the spring constant, k. Archimedes principle states that when a body is completely or partly submerged in a fluid it experiences an upthrust (a force) which is equal to the weight of fluid displaced. Therefore it is possible to find the weight of the fluid displaced if the upthrust produced by a weight placed into a fluid was known.

Method 1:

Name: Brandon Sookdeo 1. Apparatus was set up as shown in Diagram 1. 2. Readings were taken at pointers A and B without any weights attached. 3. The 50 g mass holder was then added and the new values of A and B recorded. 4. 50 g masses were then continually added one by one and readings were taken for the resulting values of A and B. Method 2: 1. All the masses were placed onto the mass holder (total mass = 300 g) and mass holder was placed onto the spring. The readings at pointers A and B were recorded. 2. A beaker was half filled with water and placed under the mass as shown in Diagram 2. 3. The depth, d, of the submerged part of the mass and the length, l, between the pointers were measured and recorded. 4. The position of the boss was adjusted and this procedure was repeated until 6 sets of values for d and corresponding values of l were collected and recorded.

Results 1: Table 1 showing values of mass and corresponding readings at pointers A and B along with calculated values of force and extension. Mass/kg 0.00

Pointer A/m 0.40

Pointer B/m 0.28

Force/N 0

Extension/m 0.00

Name: Brandon Sookdeo 0.05 0.10 0.15 0.20 0.25 0.30

0.40 0.40 0.40 0.40 0.40 0.40

0.26 0.24 0.22 0.20 0.18 0.16

0.50 1.00 1.50 2.00 2.50 3.00

0.02 0.04 0.06 0.08 0.10 0.12

Results 2: Table 2 showing values of depth and corresponding values of length between pointers A and B. d/m

l/m

0.005 0.010 0.015 0.030 0.035 0.040

0.240 0.238 0.236 0.230 0.228 0.226

Variables: Manipulated: 1. Mass 2. Depth Responding: 1. Distance between pointers A and B 2. Length Constant: Acceleration due to gravity

Name: Brandon Sookdeo Treatment of results 1: y2 − y1 x2 −x1

Gradient =

3.00−0.25 0.12−0.010

=

= 25.0 Nm-1 Therefore the spring constant of the spring is 25.0 Nm-1.

Area =

πD 4

2

¿ 8.93 ×10−4 m2

Treatment of results 2:

gradient=

¿

y 2− y 1 x 2−x 1

0.240−0.226 0.00−0.040

¿−¿ 0.35 Consider the equation:

Name: Brandon Sookdeo l=

−ρw Agd +c k

Where, ρW =density of water

A = cross sectional area of mass g = acceleration due to gravity (9.81 ms-2) d = diameter of mass k = spring constant c = a constant A graph was plotted of l vs d

Gradient of line ¿

−ρw Ag k

This can be rearranged to make,

−ρw =

gradient × k Ag

Therefore,

Name: Brandon Sookdeo −ρw =

−0.35 ×25.0 −4 8.93× 10 × 9.80

ρw =999.8 kg m−3

Error Calculation: δρ δm δk δA = + + ρ m k A

δρ 2 δ ∆ l 2 δ ∆ d 2 δ ∆ F 2 δ ∆ l 2 δr = + + + + ρ ∆l ∆d ∆F ∆l r

δρ 2 ( 0.001 ) 2 ( 0.001 ) 2 ( 0.05 ) 2 ( 0.001 ) 2 ( 0.0001 ) = + + + + ρ 0.014 0−040 2.75 0.09 0.02

δρ =0.321 ρ

−3

δρ=( 0.321 ) ( 999.8 )=321.1 kgm

Precautions: 1. All readings during experiment were taken at eye level to avoid parallax error.

Name: Brandon Sookdeo 2. It was ensured that the beaker was not filled with too much water as this could cause the water to overflow once the masses are lowered into the beaker.

Sources of error: 1. When taking reading for depth at which masses were placed in beaker of water, the light from the pencil is refracted as it passes from the water to the glass to air, causing it to be displaced. This may lead to inaccurate measurements being taken. 2. Some changes in length when the masses are lowered into the beaker were very subtle and were not recorded as there went unnoticed.

Conclusion: −1 1. Spring constant is found to be 25.0 N m

2.

Density of water was found to be 999.8 ± 321.1 kgm-3

View more...
50 cm rule Retort stands (2) Spring Pointer (2) Masses Mass holder Beaker Vernier callipers Water

Diagram 1:

Name: Brandon Sookdeo

Figure 1 showing setup of apparatus to determine the spring constant of a spring. Diagram 2:

Figure 2 showing the setup of apparatus to determine the density of water.

Name: Brandon Sookdeo Theory: Hooke’s law states the up to some maximum load (known as the limit of proportionality) the extension of a wire or spring is proportional to the applied load. Hooke's law can be written as: F = ke Where F = force applied to the spring k is the spring constant e is extension = new length - original length There are two different types of deformation 1. Elastic deformation where the material returns to its original length when the force applied is removed. 2. Plastic deformation where the material retains some of the extension even after the force is removed. By plotting a force extension graph (F vs e) and finding the gradient of the line produced one can find the spring constant, k. Archimedes principle states that when a body is completely or partly submerged in a fluid it experiences an upthrust (a force) which is equal to the weight of fluid displaced. Therefore it is possible to find the weight of the fluid displaced if the upthrust produced by a weight placed into a fluid was known.

Method 1:

Name: Brandon Sookdeo 1. Apparatus was set up as shown in Diagram 1. 2. Readings were taken at pointers A and B without any weights attached. 3. The 50 g mass holder was then added and the new values of A and B recorded. 4. 50 g masses were then continually added one by one and readings were taken for the resulting values of A and B. Method 2: 1. All the masses were placed onto the mass holder (total mass = 300 g) and mass holder was placed onto the spring. The readings at pointers A and B were recorded. 2. A beaker was half filled with water and placed under the mass as shown in Diagram 2. 3. The depth, d, of the submerged part of the mass and the length, l, between the pointers were measured and recorded. 4. The position of the boss was adjusted and this procedure was repeated until 6 sets of values for d and corresponding values of l were collected and recorded.

Results 1: Table 1 showing values of mass and corresponding readings at pointers A and B along with calculated values of force and extension. Mass/kg 0.00

Pointer A/m 0.40

Pointer B/m 0.28

Force/N 0

Extension/m 0.00

Name: Brandon Sookdeo 0.05 0.10 0.15 0.20 0.25 0.30

0.40 0.40 0.40 0.40 0.40 0.40

0.26 0.24 0.22 0.20 0.18 0.16

0.50 1.00 1.50 2.00 2.50 3.00

0.02 0.04 0.06 0.08 0.10 0.12

Results 2: Table 2 showing values of depth and corresponding values of length between pointers A and B. d/m

l/m

0.005 0.010 0.015 0.030 0.035 0.040

0.240 0.238 0.236 0.230 0.228 0.226

Variables: Manipulated: 1. Mass 2. Depth Responding: 1. Distance between pointers A and B 2. Length Constant: Acceleration due to gravity

Name: Brandon Sookdeo Treatment of results 1: y2 − y1 x2 −x1

Gradient =

3.00−0.25 0.12−0.010

=

= 25.0 Nm-1 Therefore the spring constant of the spring is 25.0 Nm-1.

Area =

πD 4

2

¿ 8.93 ×10−4 m2

Treatment of results 2:

gradient=

¿

y 2− y 1 x 2−x 1

0.240−0.226 0.00−0.040

¿−¿ 0.35 Consider the equation:

Name: Brandon Sookdeo l=

−ρw Agd +c k

Where, ρW =density of water

A = cross sectional area of mass g = acceleration due to gravity (9.81 ms-2) d = diameter of mass k = spring constant c = a constant A graph was plotted of l vs d

Gradient of line ¿

−ρw Ag k

This can be rearranged to make,

−ρw =

gradient × k Ag

Therefore,

Name: Brandon Sookdeo −ρw =

−0.35 ×25.0 −4 8.93× 10 × 9.80

ρw =999.8 kg m−3

Error Calculation: δρ δm δk δA = + + ρ m k A

δρ 2 δ ∆ l 2 δ ∆ d 2 δ ∆ F 2 δ ∆ l 2 δr = + + + + ρ ∆l ∆d ∆F ∆l r

δρ 2 ( 0.001 ) 2 ( 0.001 ) 2 ( 0.05 ) 2 ( 0.001 ) 2 ( 0.0001 ) = + + + + ρ 0.014 0−040 2.75 0.09 0.02

δρ =0.321 ρ

−3

δρ=( 0.321 ) ( 999.8 )=321.1 kgm

Precautions: 1. All readings during experiment were taken at eye level to avoid parallax error.

Name: Brandon Sookdeo 2. It was ensured that the beaker was not filled with too much water as this could cause the water to overflow once the masses are lowered into the beaker.

Sources of error: 1. When taking reading for depth at which masses were placed in beaker of water, the light from the pencil is refracted as it passes from the water to the glass to air, causing it to be displaced. This may lead to inaccurate measurements being taken. 2. Some changes in length when the masses are lowered into the beaker were very subtle and were not recorded as there went unnoticed.

Conclusion: −1 1. Spring constant is found to be 25.0 N m

2.

Density of water was found to be 999.8 ± 321.1 kgm-3

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