Question

error analysis: list at least one source of error or more you can come up with more legitimate error.
conclusion:
analysis and questions: rewrite questions before you answer.

1. what direction does the weight (force) act and what direction does the spring force act?
2. what is the name for the quantity represented by the slope? write a sentence describing the physical meaning of the slope and/or what it means for the spring physically.
3. how much force would it take to stretch your spring by 0.2 m? show your work.
4. does your spring obey hookes law? cite the relevant feature about your graph to answer this question.
5. why are springs ideal for measuring weight?

Explanation:

Step1: Analyze force directions

The weight (force due to gravity) acts vertically downwards. The spring - force acts in the opposite direction to the displacement of the spring from its equilibrium position. If the spring is stretched downwards, the spring - force acts upwards.

Step2: Identify slope quantity

The slope of the force - displacement graph for a spring represents the spring constant ($k$). Physically, it means the amount of force required to stretch or compress the spring by a unit distance. Mathematically, from Hooke's Law $F = kx$, where $F$ is the force applied, $x$ is the displacement from the equilibrium position, and $k$ is the spring constant.

Step3: Calculate force for a given displacement

Using Hooke's Law $F=kx$. If we know the value of the spring constant $k$ (from the slope of the $F - x$ graph), and $x = 0.2m$, then $F=k\times0.2$. For example, if $k = 50N/m$, then $F=50\times0.2=10N$.

Step4: Check Hooke's Law compliance

If the force - displacement graph of the spring is a straight line passing through the origin, then the spring obeys Hooke's Law. This is because Hooke's Law $F = kx$ is a linear relationship with a zero - intercept when the spring is in its equilibrium position ($x = 0$ and $F = 0$).

Step5: Explain springs as weight measurers

Springs are ideal for measuring weight because, according to Hooke's Law, the force exerted by the spring is directly proportional to the displacement. When an object is attached to a spring and the spring is in equilibrium, the force exerted by the spring is equal to the weight of the object. So, by measuring the displacement of the spring, we can determine the weight of the object.

Answer:

1. The weight acts vertically downwards. The spring - force acts in the opposite direction to the displacement of the spring from its equilibrium position.
2. The quantity represented by the slope is the spring constant ($k$). Physically, it is the force required to stretch or compress the spring by a unit distance.
3. Use $F = kx$, substitute $x = 0.2m$ and the known value of $k$ to calculate the force.
4. If the $F - x$ graph is a straight line passing through the origin, the spring obeys Hooke's Law.
5. Springs are ideal for measuring weight because the force exerted by the spring is directly proportional to the displacement and at equilibrium, the spring - force equals the weight of the object.