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Answer :
The spring constant is (a) 1631 N/m.
(b) the length of the spring when the 185 N weight is applied is 11.3 cm.
To find the spring constant, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. Hooke's Law can be written as:
F = k * x
Where:
F is the force applied to the spring,
k is the spring constant, and
x is the displacement of the spring.
In this case, the displacement of the spring is the difference between its stretched and unstretched lengths:
x = 26.1 cm - 21.0 cm = 5.1 cm = 0.051 m
The force applied to the spring is the weight of the 8.50 kg mass:
F = m * g = 8.50 kg * 9.8 m/s² = 83.3 N
we can use Hooke's Law to find the spring constant:
83.3 N = k * 0.051 m
k = 83.3 N / 0.051 m = 1631 N/m
Therefore, the spring constant is 1631 N/m.
(b) To find the length of the spring when the weight is replaced with a 185 N weight, we can use the same formula as before. The force applied to the spring is now 185 N. We need to find the displacement of the spring.
Using Hooke's Law:
185 N = k * x
x = 185 N / 1631 N/m = 0.113 m = 11.3 cm
Therefore, the length of the spring when the 185 N weight is applied is 11.3 cm.
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(a) the spring constant is 1662.75 N/m, and (b) the length of the spring is 11.1 cm when a 185 N weight is applied.
(a) The spring constant can be calculated using Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. Mathematically, this can be expressed as F = kx, where F is the force applied, k is the spring constant, and x is the displacement.
In this case, we are given the displacement of the spring (26.1 cm - 21.0 cm = 5.1 cm) and the mass hanging from the spring (8.50 kg). Since weight (W) is equal to mass (m) multiplied by the acceleration due to gravity (g), we can determine the force applied to the spring: F = mg.
First, let's convert the displacement from centimeters to meters: x = 5.1 cm = 0.051 m.
Now, we can calculate the spring constant: k = F / x = mg / x = (8.50 kg) * (9.8 m/s^2) / (0.051 m) = 1662.75 N/m.
Therefore, the spring constant is 1662.75 N/m.
(b) To find the length of the spring when a 185 N weight is applied, we can use the same formula as before: F = kx. Rearranging the equation to solve for x, we have x = F / k.
Substituting the given values into the equation: x = (185 N) / (1662.75 N/m) = 0.111 m.
Finally, we need to convert the displacement back to centimeters: x = 0.111 m = 11.1 cm.
Therefore, the length of the spring, when a 185 N weight is applied, is 11.1 cm.
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