(Moe Yanant Htoo) U3 A8 (SPH4U) assignment
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School
Ontario High School, Ontario**We aren't endorsed by this school
Course
PHYSICS SPH4U
Subject
Physics
Date
Dec 17, 2024
Pages
6
Uploaded by MinisterPower14627
1Moe Yanant HtooMoe Yanant HtooTr. Tina Wang SPH4U14thDecember 2024SPH4U SPRING CONSTANT “K” LAB U3A8 PURPOSE:To determine the spring constant of three different springs varied in size from small, medium and large. ABSTRACT: In a relaxed state, with no force applied to it, a spring remains at rest. Suppose the spring was pulled with a force, Fpull, causing the spring to stretch to the right. When stretched, the spring exerts a force, Fspring, to the left. If you push on the spring with a force, Fpush, it compresses to the left. When compressed, the spring exerts a force, Fspring, to the right. In both cases, Fspring, is called the restorative force because it restores the spring back to its original length. The amount of force exerted by a spring is proportional to the spring’s displacement; this is known as Hooke’s Law. In this equation, , is the force (measured in Newtons) exerted by the spring by a stretch, and(measured in meters) is the displacement of the spring from its original, equilibrium position.The constant of proportionality, or the stiffness of the spring, is called the spring constant and it is expressed as the variable, . Spring that have a larger value for require more force to extend or compress them which is measured by the . Springs that stretch easier have a smaller value and that is apparent in the . An essential feature to Hooke’s law is that the direction of the spring force is opposite to the direction of displacement from the original, equilibrium spring. If is upward, then is downward. If is downward, then is upward. In this lab, a mass, m, is attached to the lower end of a spring suspended from an apparatus.This causes the spring to stretch from its original, equilibrium position, a distance, d, to a new position under the influence of a load from the mass. According to Hooke’s law, the direction of the force is opposite to the direction of displacement of the spring; the direction of force is upward whereas the direction for the displacement of the spring is downward. Theforce applied by the spring must balance the upward restoring force of the spring and thus can be calculated using the equation: M*g (mass x gravity)The displacement of the spring can be calculated using the following equation:
2Moe Yanant HtooD = 𝑥i − 𝑥ƒ The values can than be inserted into Microsoft Excel, producing a line graph. The slope of the line graph produced is the k value of the spring. The k value is measured in N/m (Newtons/meter). MATERIALS: 3 different springs with variables sizes (small, medium, and large)Apparatus stand One rod that fits into the apparatus standClampRulerMasses that vary in weightComputer with Microsoft excelNote: Students could do this experiment on the following website if the above materials are not available. https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-and-springs_en.html PROCEDURE:1.First, took the rod and insert it into the apparatus stand 2.Second, used a rotating clamp to screw one end of the clamp onto the top of the rod and clamped the other end of the clamp onto the ruler. The ruler and rod stayed standing fairly parallel to one another 3.It was helpful to have the clamp clamped onto the ruler at a whole value because that was the xi value each spring test begun from 4.Third, the spring being tested was hung from the space between the rod and the ruler 5.Fourth, at the end of the spring was a hook (which may need to be attached to the spring depending on the spring being used) which the mass could freely hang from 6.Then, the equilibrium measurement of the spring was taken, which is how far down the ruler the bottom of the spring was at rest 7.Next, a mass, m, was latched onto the hook and the spring elongated a specific
3Moe Yanant Htoodistance, d 8.Mass, m, in kilograms was recorded onto a spreadsheet and so was the distance the spring elongated following the addition of the mass, d, in meters 9. Experiment was repeated five times for every spring. Each trial consisted of a different mass 10. Finally, all data was imported onto a spreadsheet in Microsoft Excel and was graphed. A k value was then recorded using by looking at the slope of the line graphed. ** Remember that the graphs are supposed to relate force to displacement in order to calculate the k value of the spring. This being said, the mass that was hung from each springmust be used to find the force applied on the spring. Use the equation, F=mg, to calculate force. OBSERVATION/RESULTS: Table 1. Spring 1-Small (Equilibrium: 0.48 m)Length (m)Force (N)0.339800.4112250.49514700.57517150.661960
4Moe Yanant Htook= Force (N)/ Length (m) = 245/0.085 = 2882 N Table 2. Spring 2- Medium (Equilibrium: 0.48 m)Length (m)Force (N)0.1459800.1812250.21514700.2517150.2851960Force (N)
5Moe Yanant Htook= Force (N)/ Length (m) = 245/0.035 = 7000 N Table 3. Spring 3-Large (Equilibrium: 0.48 m)Length (m)Force (N)0.0859800.10512250.12514700.14517150.1651960
6Moe Yanant Htook= Force (N)/ Length (m) = 245/0.02 = 12250 N ANALYSIS/CONCLUSIONS: The force applied onto a spring is directly proportional to its displacement. When dividing the applied force (N) by the displacement (m) will give the spring constant (N/m). And the spring constant remains still until the spring becomes deformed after it went pass the elastic limit. And when graphing, the slope before the elastic limit, it is equal to that of the spring constant. And the smaller the spring constant, the longer the displacement of the spring is. It can be seen in the three tables above, where the spring stretched 0.33m, 0.145m and 0.085 from the smallest to the largest spring constant for the same weight of 980 N.ERROR ANALYSIS: There can be error when reading the precise measurement, due to human’s eye. But we can makesure the data is correct by repeating multiple reading and calculations and take the average reading. And estimating decimals places can also results in tiny errors.