A load of 80N extends a spring by 8cm. When the load is replaced by a copper block, the extension produced is 10cm. Calculate the weight of the copper block, assuming that the elastic limit of the spring is not exceeded.
F=ke right? So we are looking for f2 where f1 = 80N, e1 = 8cm and e2 = 10cm :. k= f/e then we have f1/e1 = f2/e2 :. We have 80/8=x/10 where x = 100
I need the calculation and the answer
To solve this problem, we need to use Hooke's Law, which states that the extension of a spring is directly proportional to the load applied, as long as the elastic limit of the spring is not exceeded. The formula for Hooke's Law is:
F = kx
Where:
F = force applied on the spring (load)
k = spring constant (a measure of the stiffness of the spring)
x = extension of the spring
In this case, the load is 80N, and it extends the spring by 8cm. We can use these values to find the spring constant (k).
80N = k * 0.08m (converting cm to m)
Rearranging the equation gives:
k = 80N / 0.08m = 1000 N/m
Now, let's use the spring constant to find the weight of the copper block when it extends the spring by 10cm.
W = k * x
W = 1000 N/m * 0.10m = 100N
Therefore, the weight of the copper block is 100N.
x/10 = 80/8
Well, well, well. Looks like we're springing into action with this question!
First things first, let's use Hooke's Law to tackle this. Hooke's Law states that the extension produced in a spring is directly proportional to the applied force.
We have two scenarios here: one with the load and one with the copper block.
For the load, we have a force of 80N and an extension of 8cm. So, using Hooke's Law, we can calculate the spring constant (k). Kudos to the load for being such a great sport!
80N = k * 0.08m (we converted 8cm to meters)
Next up, we have the copper block. We know that the extension produced when the copper block is applied is 10cm. But we need to find the weight of the copper block.
Now, here comes the funny part. Copper is known for being heavy, but it won't be offended if we ask it to step on the scale. To find the weight, we need to calculate the force applied by the copper block, which is equal to its weight.
So, let's plug in the values we have into our fantastic equation:
Force = k * Extension
Force = k * 0.1m (we converted 10cm to meters)
Now, since the force applied is equal to the weight of the copper block, we can rewrite the equation as:
Weight of Copper Block = k * 0.1m
But wait, we can substitute the value of k from our first equation:
Weight of Copper Block = 80N / 0.08m * 0.1m
And here's where the magic happens:
Weight of Copper Block = 100N
Voila! The weight of the copper block is 100N. Time to give that copper block a round of applause for weighing in on this question!
Remember, never underestimate the power of a spring and a good old-fashioned calculation. Keep on bouncing with more questions, and I'll be here cracking jokes and providing answers!