The text says: "The teacher decided to check if Hooke's law is valid for hair elastics. In the office, she took a set of identical weights, each weighing 50 g, and started hanging them on the elastic band. Determine, if possible, based on the available data, whether Hooke's law is valid for the elastic band being studied. Answer briefly with an explanation. And below is a table: Number of suspended weights Length of the elastic band, cm 1 8 2 9 3 11 4 13 5 14

Analysis of the data:

• Hooke's Law states that the force applied to a spring (or elastic band) is directly proportional to the extension (or stretch) of the spring. Mathematically, this is represented as F = kx, where F is the force, k is the spring constant, and x is the extension.
• In this experiment, the force is applied by the weights. Since each weight is 50 g, the force is proportional to the number of weights.
• The extension of the elastic band is the difference between its length under load and its original length. We need to determine the original length first.

Calculations:

Let's assume the original length of the elastic band is $$L_0$$. The extension ($$x$$) for each number of weights ($$n$$) is $$(L - L_0)$$, where $$L$$ is the measured length.

The force ($$F$$) is proportional to the number of weights ($$n$$). Let the force of one weight be $$F_w$$. So, $$F = n imes F_w$$.

According to Hooke's Law, $$F = kx$$, so $$n imes F_w = k(L - L_0)$$.

We can analyze the relationship between the number of weights and the extension. If Hooke's law holds, then the ratio of force to extension should be constant (k).

Let's examine the increments:

• From 1 to 2 weights: Force increases by $$F_w$$. Length increases from 8 cm to 9 cm (1 cm increase).
• From 2 to 3 weights: Force increases by $$F_w$$. Length increases from 9 cm to 11 cm (2 cm increase).
• From 3 to 4 weights: Force increases by $$F_w$$. Length increases from 11 cm to 13 cm (2 cm increase).
• From 4 to 5 weights: Force increases by $$F_w$$. Length increases from 13 cm to 14 cm (1 cm increase).

The increase in length is not proportional to the increase in the number of weights (and thus force). For instance, when the number of weights doubled from 2 to 4, the length increased from 9 cm to 13 cm (4 cm increase). If it were proportional, and assuming some initial length, the extension should double as well.

Let's try to find an initial length $$L_0$$. If we assume the relationship is linear for some range, we can see the changes.

If Hooke's law applies, the extension should be proportional to the force. Let's check the ratio of length increase to the increase in the number of weights:

• (9-8) cm / (2-1) = 1 cm/weight
• (11-9) cm / (3-2) = 2 cm/weight
• (13-11) cm / (4-3) = 2 cm/weight
• (14-13) cm / (5-4) = 1 cm/weight

Since the increase in length per added weight is not constant, Hooke's law is not strictly followed across the entire range of data.

The increments are not consistent (1, 2, 2, 1 cm for each additional 50g weight). This indicates that the elastic band is either not behaving according to Hooke's Law, or there are other factors influencing the measurement, or the data itself is not perfectly linear.

Conclusion:

Based on the inconsistent increases in the length of the elastic band for each added weight, it cannot be concluded that Hooke's law is strictly followed for this elastic band in the given experiment.

Answer: No, Hooke's law is not strictly followed because the increase in the length of the elastic band is not directly proportional to the increase in the number of suspended weights.