A Level Physics Practice Exam

What determines the total energy stored in the rope when it is under tension?

1. The amount of extension and the stiffness of the rope

2. The weight of the rope alone

3. The temperature of the rope

4. Only the length of the rope

The correct answer is: The amount of extension and the stiffness of the rope

The total energy stored in a rope under tension is primarily determined by the amount of extension the rope experiences and its stiffness, which is a measure of how much force is needed to extend the rope by a certain amount. This relationship is described by Hooke's Law, which states that the force exerted by a spring (or a rope acting like a spring) is proportional to its extension, as long as it remains within its elastic limit. The energy stored can be quantified using the formula for elastic potential energy, which is given by \( \frac{1}{2} k x^2 \), where \( k \) is the stiffness (spring constant) of the rope and \( x \) is the amount of extension. Therefore, both the amount the rope is stretched (extension) and its material properties (stiffness) combine to determine how much energy is stored in the rope when it is stretched. Other factors listed, such as the weight of the rope, its temperature, and its length, do not directly determine the elastic potential energy stored in the rope under tension. The weight might contribute to how much tension is applied if the rope is suspended, but it does not influence the intrinsic energy storage characteristics of the rope itself. Similarly,