A spring of natural length 30cm is stretched to 35cm by a load of 15N. Calculate the extension produced,the elastic constant of the spring,the work done in stretching the spring.
the spring stretched by x=5 cm
F = kx
so now you can find k
work = 1/2 kx^2
watch the units
a. d = 35-30 = 5 cm stretched.
b. k = F/d = 15/5 = 3N/cm = 300N./m.
c. W = F*d = 15*0.05 = 0.75 J.
No
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Because it had way too many problems!
Now let's solve your problem.
To find the extension produced, we subtract the natural length from the stretched length:
Extension = Stretched length - Natural length
Extension = 35 cm - 30 cm
Extension = 5 cm
So, the extension produced is 5 cm.
Next, let's find the elastic constant, also known as the spring constant. It is defined as the ratio of the force applied to the extension produced.
Elastic constant = Force / Extension
Elastic constant = 15 N / 5 cm
Oops! We need to convert the extension to meters first!
1 cm = 0.01 m
5 cm = 5 * 0.01 m = 0.05 m
Elastic constant = 15 N / 0.05 m
Elastic constant = 300 N/m
Therefore, the elastic constant of the spring is 300 N/m.
Finally, let's calculate the work done in stretching the spring. The work done is equal to the force applied multiplied by the distance over which the force is exerted.
Work = Force * Distance
Work = 15 N * 0.05 m
Work = 0.75 J
So, the work done in stretching the spring is 0.75 Joules.
Keep up the good work, and remember to always stretch your problems with a little humor!
To calculate the extension produced by the spring, we can use the formula:
Extension (Δx) = Final Length (Lf) - Initial Length (Li)
Given that the natural length (Li) of the spring is 30 cm and it is stretched to a length (Lf) of 35 cm, the extension can be calculated as:
Δx = 35 cm - 30 cm
= 5 cm
Therefore, the extension produced by the spring is 5 cm.
To calculate the elastic constant (k) of the spring, we can use Hooke's Law, which states that the force applied to a spring is directly proportional to the extension produced. Mathematically, it can be expressed as:
F = k * Δx
where F is the force applied to the spring, k is the elastic constant, and Δx is the extension produced.
In the given problem, a load of 15N is applied to the spring. Plugging in the values, we can rearrange the equation to solve for k:
15N = k * 5 cm
To calculate the elastic constant, we need to convert the extension from cm to meters (m) since the SI unit of force is Newtons (N). 1 cm = 0.01 m
15N = k * 0.05 m
Solving for k:
k = 15N / 0.05 m
= 300 N/m
Therefore, the elastic constant of the spring is 300 N/m.
To calculate the work done in stretching the spring, we can use the equation:
Work (W) = (1/2) * k * (Δx^2)
Substituting the values, we get:
W = (1/2) * 300 N/m * (0.05 m)^2
Simplifying the equation:
W = 0.5 * 300 N/m * 0.0025 m^2
= 0.375 J
Therefore, the work done in stretching the spring is 0.375 Joules.