If a force of 100n stretches a spring by 0.1cm. Find
(A) the elastic constant
(B) the work done in stretching the spring 0.3cm if the elastic limit is not exceeded
a)Since F = ke,
k= F/e,
But 0.1cm =0.001m
k = 100N/0.001m = 100,000N/m or 100,000Nm–¹ or 10×10⁵Nm‐¹
b)W=½Ke²
½ × 100000 × 0.003 ×0.003
0.45Nm
0.45Joules(J)
(A) since F = kx, k = 100N/0.1cm = 1000N/cm
now use that to to (B)
A force e/s 0.8n stretches an elastic spring by 2cm find the elastic constant of the spring
(A) Elastic constant? Oh, you mean the "springiness index"! Alright, let's calculate that. To find the elastic constant, we can use Hooke's Law, which states that the force applied is directly proportional to the extension of the spring.
F = k * x
Where F is the force applied, k is the elastic constant, and x is the extension. In this case, F = 100N and x = 0.1cm (or 0.001m).
Plugging in the values:
100N = k * 0.001m
Solving for k:
k = 100N / 0.001m = 100,000 N/m
So, the elastic constant of the spring is 100,000 N/m.
(B) Ah, we're stretching the spring even further now, but we need to make sure we don't exceed the elastic limit. If we assume the elastic limit is not exceeded, which is crucial, then we can calculate the work done!
We can use the formula for work done:
Work = (1/2) * k * (x^2)
Where k is the elastic constant and x is the extension. In this case, k = 100,000 N/m and x = 0.3cm (or 0.003m).
Plugging in the values:
Work = (1/2) * 100,000 N/m * (0.003m^2)
= (1/2) * 100,000 N/m * 0.000009m
= 0.45 J
So, the work done in stretching the spring 0.3cm (without exceeding the elastic limit) is approximately 0.45 Joules.
To solve this problem, we can use Hooke's Law, which states that the force needed to stretch or compress a spring is directly proportional to the displacement of the spring from its equilibrium position.
(A) To find the elastic constant (k), we can rearrange Hooke's Law equation:
F = k * x
where F is the force applied, k is the elastic constant, and x is the displacement of the spring.
In this case, F = 100 N and x = 0.1 cm = 0.001 m
Substituting these values into the equation, we have:
100 N = k * 0.001 m
To find k, we can isolate it:
k = 100 N / 0.001 m
k = 100,000 N/m
So, the elastic constant (k) is 100,000 N/m.
(B) To find the work done in stretching the spring by 0.3 cm, we use the formula for work done (W):
W = (1/2) * k * (x² - x₁²)
Where W is the work done, k is the elastic constant, x is the final displacement, and x₁ is the initial displacement.
In this case, x = 0.3 cm = 0.003 m and x₁ = 0.1 cm = 0.001 m. Substituting these values and the elastic constant (k = 100,000 N/m) into the equation, we have:
W = (1/2) * 100,000 N/m * ((0.003 m)² - (0.001 m)²)
Calculating the expression inside the parentheses, we get:
W = (1/2) * 100,000 N/m * (0.000009 m² - 0.000001 m²)
W = (1/2) * 100,000 N/m * 0.000008 m²
W = 0.5 * 100,000 N/m * 0.000008 m²
W = 400 N*m
Therefore, the work done in stretching the spring 0.3 cm is 400 N*m.