hooke's law determine that if a small weight is suspended from a spring,the length of the stretched spring y, is a linear function of the weight, x.
determine the linear equation if the unstretched spring is 12 inch and weight of 2 lbs stretches it to 16 inch
Looks like they provide data for two points. If it's a linear function, then those two points will provide the equation for the line.
Two points (0,12)(2,16)
Letting y be the length,
(y-12)/(x-0) = (16-12)/(2-0)
(y-12)/x = 4/2
y-12 = 2x
y = 2x + 12
To determine the linear equation for Hooke's law in this scenario, we need to use the given information about the unstretched and stretched lengths of the spring.
Let's denote the weight as x (in lbs) and the length of the stretched spring as y (in inches). According to Hooke's law, the relationship between y and x should be linear.
Given:
Unstretched length of the spring (y when x = 0): 12 inches
Length of the stretched spring when the weight is 2 lbs (y when x = 2): 16 inches
To form a linear equation, we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. In this case, we want to find the equation for y in terms of x.
First, let's find the slope:
Slope (m) = (change in y) / (change in x)
Slope (m) = (16 - 12) / (2 - 0) = 4 / 2 = 2
Now, let's find the y-intercept (b) using one of the given points:
Using the point (x = 0, y = 12):
y = mx + b
12 = 2(0) + b
12 = 0 + b
b = 12
Thus, the linear equation representing Hooke's law in this scenario is:
y = 2x + 12