Final answer:
The distance between the 4N and 9N marks on a spring with a force constant of 150 N/m is 3.33 centimeters.
Step-by-step explanation:
To calculate the distance between the 4N and 9N marks on a spring with a force constant of 150 N/m, we use Hooke's Law, which states that the force (F) applied to stretch or compress a spring is directly proportional to the distance (x) the spring is stretched or compressed from its natural length. The formula is F = kx, where k is the spring constant.
First, we calculate the distance for 4N force:
- 4N = 150 N/m × x
- x = 4N / 150 N/m
- x = 0.0267m or 2.67cm
Next, for the 9N force:
- 9N = 150 N/m × x
- x = 9N / 150 N/m
- x = 0.06m or 6cm
The distance between the 4N and 9N marks:
- Distance = 6cm - 2.67cm
- Distance = 3.33cm
Therefore, the 4N and 9N marks will be 3.33 centimeters apart on the newton metre.