The Physics of a Spanner: Understanding Torque
Ever wondered why it's easier to loosen a stubborn nut with a longer wrench? The answer isn't magic; it's physics! Specifically, it's a fundamental concept called torque, or the moment of force.
Torque is the measure of the force that can cause an object to rotate around an axis. Think of it as a "turning" or "twisting" force. It’s at play in many of our daily activities, from pushing open a door (you push farthest from the hinges, right?) to pedaling a bicycle.
To see this principle in action, let's break down a classic physics problem.
The Problem
A mechanic unscrews a nut by applying a force of 140 Newtons (N) with a spanner that is 40 centimeters (cm) long.
Question: What should be the length of the spanner if a force of only 40 N is applied to unscrew the exact same nut?
The Science Behind the Solution
To loosen the nut, a specific amount of torque is required. This required torque is a constant. It doesn't change whether you use a short spanner with a lot of force or a long spanner with less force. The turning effect must be the same.
The formula for torque is simple:
$$Torque = Force \times \text{Perpendicular Distance from the pivot}$$
In our case, the "distance" is the length of the spanner. Let's call our first scenario (Case 1) and our second scenario (Case 2). The core principle is:
$$Torque_1 = Torque_2$$
Which means:
$$(Force_1 \times \text{Length}_1) = (Force_2 \times \text{Length}_2)$$
Solving the Problem Step-by-Step
Let's list what we know:
- Force 1 ($F_1$): 140 N
- Length 1 ($d_1$): 40 cm
- Force 2 ($F_2$): 40 N
- Length 2 ($d_2$): ? (This is what we need to find)
Now, we plug these values into our equation:
$$F_1 \times d_1 = F_2 \times d_2$$
$$140 \text{ N} \times 40 \text{ cm} = 40 \text{ N} \times d_2$$
To solve for $d_2$, we can rearrange the equation:
$$d_2 = \frac{(140 \text{ N} \times 40 \text{ cm})}{40 \text{ N}}$$
As you can see, the "40 N" on the top and bottom of the fraction cancel each other out.
$$d_2 = 140 \text{ cm}$$
Answer: The mechanic would need a spanner that is 140 cm long.
The Takeaway
This problem beautifully illustrates the inverse relationship between force and the length of the lever arm when torque is constant.
- Less force? You need a longer lever.
- Shorter lever? You need to apply more force.
So, the next time you're struggling with a tight bolt, remember your physics lesson and grab a longer wrench!