There is a vertical tension at the top of a 4 m long ladder holding it at an incline. The bottom of the ladder is touching the floor, which exerts a normal force. You are standing 1 meter from the top of the ladder. What happens to the tension as you walk up the ladder? As you walk down the ladder? As the angle between the ladder and the ground decreases? Why?
To understand what happens to the tension as you walk up or down the ladder, or as the angle between the ladder and the ground decreases, let's break down the forces acting on the ladder.
When the ladder is in equilibrium (not moving), the forces acting on it are the vertical tension at the top, the weight of the ladder acting downward, and the normal force exerted by the floor upward.
As you walk up the ladder, your weight adds to the tension force because you're applying an additional downward force at a point lower on the ladder. This increases the overall tension in the ladder. So, as you walk up the ladder, the tension force increases.
Conversely, as you walk down the ladder, your weight reduces the tension force because you're applying an additional downward force at a point higher on the ladder. This decreases the overall tension in the ladder. Therefore, as you walk down the ladder, the tension force decreases.
Now, let's consider the effect of reducing the angle between the ladder and the ground. As the angle decreases, the vertical component of the tension force decreases. This is because the vertical component of the tension force is responsible for balancing the weight of the ladder. As the angle becomes smaller, the vertical component of the tension force becomes smaller, reducing the overall tension in the ladder.
In summary:
- As you walk up the ladder, the tension force increases because your weight adds to the tension force.
- As you walk down the ladder, the tension force decreases because your weight reduces the tension force.
- As the angle between the ladder and the ground decreases, the tension force decreases because the vertical component of the tension force decreases.
These changes occur because the tension force needs to counterbalance the additional weights or compensate for the decrease in the vertical component to maintain the ladder's equilibrium.