hooke's law the distance d when a spring is stretched by a hanging object. if the distance is 14cm when the weight is 4kg what is the distance when the weight is 9kg The distance is
4/14 = 9/d,
4d = 9*14 = 126,
d = 31.5 cm.
To solve this problem, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the distance it is stretched or compressed. Mathematically, this can be represented as:
F = k * d
where F is the force applied to the spring, k is the spring constant, and d is the distance the spring is stretched or compressed.
In the given problem, the distance (d1) is 14 cm when the weight (W1) is 4 kg. We need to find the distance (d2) when the weight (W2) is 9 kg.
Now, let's set up an equation using Hooke's Law:
F1 = k * d1 (Equation 1)
F2 = k * d2 (Equation 2)
Since the weight is acting as the force applied to the spring, we can rewrite the equations as:
W1 = k * d1 (Equation 3)
W2 = k * d2 (Equation 4)
We know that the weight (W2) is 9 kg, so we can rewrite Equation 4 as:
9 kg = k * d2
To find the value of the spring constant (k), we need to use Equation 3 with the given values:
4 kg = k * 14 cm
Now, we can solve for k by dividing both sides of the equation by 14 cm:
k = 4 kg / 14 cm
Once you calculate the value of k, you can substitute it into Equation 4 to find the distance (d2) for W2:
9 kg = k * d2
Substitute the value of k and rearrange the equation to solve for d2:
d2 = 9 kg / k
Calculate the value of d2 using the previously calculated value of k.
By following these steps, you can find the distance when the weight is 9 kg.
In Hooke's Law, the force experienced by a spring when it is stretched or compressed is directly proportional to the distance it is stretched or compressed.
We can use the formula for Hooke's Law, which is F = k * x, where F represents the force, k represents the spring constant, and x represents the distance the spring is stretched or compressed.
To find the distance when the weight is 9kg, we can set up a proportion using the given information:
4kg / 14cm = 9kg / x
Now we can cross-multiply and solve for x:
4kg * x = 14cm * 9kg
4x = 126kg * cm
To convert kg * cm to kg * m (which is the SI unit for force):
1 kg * cm = 0.01 kg * m
So,
4x = 126kg * cm * 0.01 kg * m
4x = 1.26 kg * m
Dividing both sides of the equation by 4:
x = 1.26 kg * m / 4
x = 0.315 kg * m
Therefore, the distance when the weight is 9kg is 0.315 kg * m.