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• Publicado : 5 de diciembre de 2011

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Abstract:

The objective of this experiment is to study tension by using three different rubber rods.
Different amounts of weights will be added to these rubbers, the final length of the rubber rod will be measured, and the final diameter will also be recorded. The data will be used to calculate the measured elongation and theoretical elongation and modulus of elasticity of each rubberrod. After, graphs and tables are drawn, Hooke‘s law is used to determine if the results collected is similar in each case. The experiment will show that the elongation depends on the modulus of elasticity of rubber.

Introduction:
When a structural member, such as a rope, cable, rubber or other such object, is attached to a body or weight and pulled taut, the cord pulls on the body with a forcedirected away from the body and along the cord. The force is called tension. As a result, the structural member’s dimensions will change when forces act on it. Its length will increase, and the cross sectional area will decrease. In this experiment, we use Hooke’s law to understand tension loading and how the cross sectional area and the original length relate to elongation. Hooke’s lawstates that the elongation is proportional to the force which describes the elastic, linear behavior of a material. In this experiment, weights ranging from 2 to 6 lbs are added to three different
rubbers. The elongation, original length, and diameter are measured and recorded. The following formulas and symbols were used:
Formulas ∕ symbols | Unit | Definition |
σ = Eε | psi (lb∕in.2) | Therelationship between strain and normal stress. |
σ = PA | psi (lb∕in.2) | Normal stress is the magnitude of the force divided by the cross sectional area of the member perpendicular to direction of the applied force. |
P | lb. | The magnitude of the force. |
Ao = (πDo2) ∕ 4 | ln.2 | The initial cross sectional area of the rubber |
ε = (∆l ∕ lo ) | | Strain is the ratio of change in lengthof rubber to the initial length of unloaded rubber. |
(∆l = l − lo ) | in. | The measured elongation formula (change in length of rubber). |
∆l = (P lo) ∕ (AE) | in. | Theoretical elongation formula defined as a function of the load applied, the cross sectional area, the length, and the type of the material the member is made of. |
l | in. | The final length of loaded rubber rod. |lo | in. | The initial length of rubber |
E | psi (lb∕in.2) | Modulus of elasticity of rubber |
A =(πD2) ∕ 4 | in.2 | Final sectional area of rubber. |
Do | in. | The initial diameter of rubber |
D | in. | Final diameter of rubber |

Experimental materials:
* Three rubber rods with different length and diameter.
* Weights with 1 lb, 2 lb, and 5 lb.
* Vernier caliper
*Support stand and clamps
* Weight holder
* Tape-measure

Experimental procedure:
Case 1: (18-inch rubber rod, and its diameter is 0.2520 in.)

Hang the rubber rod from the top of the stand and the clamps. Then, hang a weight holder at the bottom of the rubber rod. A weight of 2 lb is added on the weight holder and make sure the weight holder won’t touch the table. Then, use atape-measure to measure the final length between the top and the bottom of the rubber rod, and record the data. Then, use a vernier caliper to measure the diameter of the rubber rod. When use the vernier caliper, one shouldn’t tighten the tips of the vernier caliper and make sure it is in inch mode when reading the data. The weight is increased by 1 lb until it reaches 6 lbs. Each time the final lengthand diameter have to be measured and recorded.
Case 2 (12-inch rubber rod, and its diameter is 0.2595 in.)
Repeat the procedures in case 1, and make sure to record the data.

Case 3 (12-inch rubber rod, and its diameter is 0.6335 in.)
Repeat the procedures in case 1, and make sure to record the data.
Data:

Table 1.

l (in.) | Ao = (πDo2) ∕ 4(in.2) | A=(πD2) ∕ 4 (in.2) | D...