A spring that is 0.7 m in length elongates to 1.06 m when a 20 Newton force is exerted to stretch the spring. By how much more does the spring stretch when an additional 8 Newtons of force is exerted on it?
1.01
0.053
0.072
0.45
0.144
0.561
0.736
1.06
I think there are 3 parts to figuring this out:
#1) 20 N + 8 N + 28N
#2) idk...
#3) idk...
Please help!
Extens
Extension caused by first force = 1.06-0.7=0.36cm......since F ~ e...... F= ke...... F/e = k (constant of proportionality).... F1/F2 =e1 /e2...... F2=20+8=28N......F1=20N......e1=0.36cm......e2=?....... F1/F2 =e1 /e2...... 20/28=0.36/e2.....e2=0.504......
A spiral spring is stretched 0.6cm by a force of 20N find the original Leng of the material if a force of 40N stretches a material of 30cm
To solve this problem, we need to use Hooke's Law, which states that the elongation of a spring is directly proportional to the force applied to it. Mathematically, this can be represented as:
F = k * x
Where:
F is the force applied to the spring
k is the spring constant
x is the elongation of the spring
We can rearrange this equation to solve for x:
x = F / k
Now let's break down the problem into three parts as you mentioned:
1) Calculate the spring constant (k):
To find the spring constant, we can use the given information that the spring elongates from 0.7 m to 1.06 m when a 20 N force is applied. We can write this as:
x1 = 0.36 m (elongation when 20 N force is applied)
Using the equation above, we can find k by rearranging it:
k = F / x
k = 20 N / 0.36 m
k ≈ 55.56 N/m
So the spring constant is approximately 55.56 N/m.
2) Find the elongation when an additional 8 N force is applied:
Using the same equation as before, we can calculate the elongation (x2) when an additional 8 N force is applied:
F2 = 8 N (additional force)
x2 = F2 / k
x2 = 8 N / 55.56 N/m
x2 ≈ 0.144 m
Therefore, the spring elongates by approximately 0.144 m when an additional 8 N force is applied.
3) Calculate the total elongation:
To find the total elongation, we need to add the elongations from the two forces:
Total elongation = x1 + x2
Total elongation ≈ 0.36 m + 0.144 m
Total elongation ≈ 0.504 m
So, the total elongation is approximately 0.504 m.
Based on the answer choices provided, the option closest to 0.504 m is 0.561. Therefore, the correct answer is 0.561.