A spiral spring extends by 5cm under a load of 60N.when the load is replaced by a steel block, the new extension is 7cm. Calculate the weight of the steel block.
Well, well, well! Looks like we have a springy situation here. Let's get cracking!
First things first, let's find out the change in extension. The original extension was 5 cm, and with the steel block, it became 7 cm. So, the change in extension is 7 cm - 5 cm, which is 2 cm.
Now, let's put our comedy hats on and remember Hooke's Law: "The force exerted by a spring is directly proportional to the extension." In this case, the force is the weight of the steel block. To calculate it, we need to find the proportionality constant, also known as the spring constant.
If we divide the force (60N) by the original extension (5 cm), we can find the spring constant. So, 60N divided by 5 cm gives us 12N/cm. This means that every centimeter of extension exerts a force of 12 Newtons.
Now, armed with this information, we can determine the weight of the steel block. We know that the extension increased by 2 cm, so we'll multiply that by the spring constant of 12N/cm.
2 cm multiplied by 12N/cm gives us a result of 24N. Ta-da! The weight of the steel block is 24 Newtons.
Keep in mind, though, that this calculation assumes the spring obeys Hooke's law perfectly and that there are no other external forces at play. Oh, springs and their unpredictable antics!
To solve this problem, we can use Hooke's law, which states that the force applied to a spring is directly proportional to the extension of the spring.
Let's denote:
- x1 as the initial extension of the spring (5 cm)
- F1 as the initial load (60 N)
- x2 as the new extension of the spring (7 cm)
- F2 as the weight of the steel block (to be determined)
According to Hooke's law, we have:
F = k*x
where F is the force applied, k is the spring constant, and x is the extension of the spring.
First, we can calculate the spring constant (k) using the initial load and extension:
k = F1 / x1
k = 60 N / 5 cm
Next, we can use the spring constant to find the weight of the steel block:
F2 = k * x2
F2 = (60 N / 5 cm) * 7 cm
Now, let's calculate the weight of the steel block:
F2 = (60 N / 5 cm) * 7 cm
F2 = 12 * 7
F2 = 84 N
Therefore, the weight of the steel block is 84 N.
To calculate the weight of the steel block, we need to use Hooke's law, which states that the extension of an elastic material (such as a spring) is directly proportional to the force applied to it. The formula for Hooke's law is:
F = k * Δx
Where:
F is the force applied
k is the spring constant
Δx is the extension or compression of the spring
In this case, we have two scenarios: the original load of 60N, which causes an extension of 5cm, and the steel block, which causes an extension of 7cm.
Let's start by calculating the spring constant (k) using the first scenario:
k = F / Δx
k = 60N / 0.05m
k = 1200 N/m
Now that we have the spring constant, we can use it to find the weight of the steel block using the second scenario:
F = k * Δx
F = 1200 N/m * 0.07m
F = 84N
Therefore, the weight of the steel block is 84N.
F = kx
so you want F such that
F/7 = 60/12