A rubber band of relaxed length 6.3 cm stretches to 10.2 cm under a force of 1.0 N, and to 16.5 cm under a force of 2.0 N. Does this rubber band obey Hooke's Law?

To determine if the rubber band obeys Hooke's Law, we need to check if its behavior follows the linear relationship between the force applied and the resulting stretch. According to Hooke's Law, the force is directly proportional to the stretch of a spring or an elastic material.

We can start by calculating the elongation of the rubber band for each force applied. The elongation is the difference between the stretched length and the relaxed length.

For the first force (1.0 N):
Elongation = Stretched Length - Relaxed Length
Elongation = 10.2 cm - 6.3 cm
Elongation = 3.9 cm

For the second force (2.0 N):
Elongation = Stretched Length - Relaxed Length
Elongation = 16.5 cm - 6.3 cm
Elongation = 10.2 cm

Next, we need to determine if the elongation is directly proportional to the force applied. We can do this by calculating the ratio of elongation to force for both cases.

For the first force (1.0 N):
Ratio = Elongation / Force
Ratio = 3.9 cm / 1.0 N
Ratio = 3.9 cm/N

For the second force (2.0 N):
Ratio = Elongation / Force
Ratio = 10.2 cm / 2.0 N
Ratio = 5.1 cm/N

If the rubber band obeys Hooke's Law, the ratio of elongation to force should be constant for different forces. However, in this case, we can see that the ratio changes, which means that the rubber band does not strictly follow Hooke's Law.

Therefore, based on the given information, we can conclude that the rubber band does not obey Hooke's Law.