according to Hooke's law,<em> "provided the elastic limit of an elastic material is not exceeded the the extension e is directly proportional to the applied force."</em>

$F= ke$

where F is the applied force in N

k is the spring constant N/m

e is the extension in meters

Given data

mass m= 24kg

extensnion=15cm in meters= $\frac{15}{100}$ = $0.15m$

we can solve for the spring constant k

we also know that the force F = mg

assuming $g=9.81m/s^{2}$

therefore

$24*9.81=k*0.15\\235.44=k*0.15\\k=\frac{235.44}{0.15} \\k=1569.6N/m\\$

We can use this value of k to solve for the mass that will cause an extension of $10cm= 0.1m$

$x*9.81=1569.6*0.1\\\\x= \frac{156.96}{9.81} \\\x= 16kg$

5 0

3 years ago

A polygon has the following coordinates: A(3,1), B(5,3), C(2,5), D(-1,5), E(-4,3), F(-2,1). Find the length of DC.

nlexa [21]

To find the length of a line given two points, we are going to use the distance formula, which is defined below:

$D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

( $(x_1, y_1)$ and $(x_2, y_2)$ are the two points)

The points in this problem are (2, 5) and (-1, 5). We can find the distance of DC by substituting these values into the distance formula and simplifying, as shown below:

$D = \sqrt{(-1 - 2)^2 + (5 - 5)^2$