A spring has a length of 60cm when it unstretched. A load of 10N increases its length to 64 cm and a load of 20N increases its length to 68cm

a)what extension is produced by the 20N load?
b) What length would the spring have if a load of 15N were added to it?
c) Determine the force needed to produce an extension of 1cm

0 load and length 50 what is the extension

a.F\ =\ Kx,\ x\ =\ k\ :\ f\ =\ 68.0cm\ :\ 20N\ =\ 3.4cm

b.ya

To solve this problem, we can use Hooke's Law, which states that the force applied to a spring is directly proportional to the extension of the spring. The formula for Hooke's Law is given by:

F = k * x

where F is the force applied, k is the spring constant, and x is the extension of the spring.

a) To find the extension produced by the 20N load, we need to first find the spring constant, k. We can use the first set of data points:

F1 = 10N (force)
x1 = 64cm - 60cm = 4cm (extension)

Using Hooke's Law, we can rearrange the formula to solve for k:

k = F1 / x1

k = 10N / 4cm

k = 2.5 N/cm

Now we can use the spring constant to find the extension produced by the 20N load:

F2 = 20N (force)
k = 2.5 N/cm (spring constant)

x2 = F2 / k

x2 = 20N / 2.5 N/cm

x2 = 8cm

Therefore, the extension produced by the 20N load is 8cm.

b) To find the length of the spring with a load of 15N, we need to use Hooke's Law with the spring constant that we found:

F3 = 15N (force)
k = 2.5 N/cm (spring constant)

x3 = F3 / k

x3 = 15N / 2.5 N/cm

x3 = 6cm

To find the new length, we add the extension to the unstretched length:

New length = unstretched length + extension

New length = 60cm + 6cm

New length = 66cm

Therefore, the length of the spring with a load of 15N is 66cm.

c) To determine the force needed to produce an extension of 1cm, we can use Hooke's Law with the spring constant:

x4 = 1cm (extension)
k = 2.5 N/cm (spring constant)

F4 = k * x4

F4 = 2.5 N/cm * 1cm

F4 = 2.5N

Therefore, the force needed to produce an extension of 1cm is 2.5N.