力與彈性：練習題

A student hangs a weight on a spring and it stretches. According to the syllabus, how many forces must be applied to a stationary object to change its shape by stretching or bending?

A spring has a spring constant of \( 25 \text{ N/m} \). Calculate the force required to produce an extension of \( 0.20 \text{ m} \), assuming the limit of proportionality is not exceeded.

A force of \( 12 \text{ N} \) stretches a spring from an original length of \( 10 \text{ cm} \) to a new length of \( 16 \text{ cm} \). Calculate the work done in stretching the spring, assuming it behaves elastically.

A spring has a spring constant of \( 40 \text{ N/m} \). Calculate the extension of the spring when a force of \( 10 \text{ N} \) is applied, assuming the limit of proportionality is not exceeded.

A spring with a spring constant of \( 150 \text{ N/m} \) is compressed by \( 0.10 \text{ m} \). Calculate the elastic potential energy stored in the spring.

A spring is stretched by a force of \( 4.0\text{ N} \). If the spring constant is \( 50\text{ N/m} \), calculate the extension of the spring in metres.

A spring with a spring constant of \( 150 \text{ N/m} \) is compressed by \( 0.10 \text{ m} \). Calculate the elastic potential energy stored in the spring and explain how this value would change if the compression was doubled, assuming the limit of proportionality is not exceeded.

A student investigates the extension of a spring by hanging weights from it. The spring has an original length of \( 0.15 \text{ m} \). When a mass of \( 400 \text{ g} \) is hung from the spring, the new length becomes \( 0.23 \text{ m} \). Assume the limit of proportionality is not exceeded and use \( g = 9.8 \text{ N/kg} \).

a) Calculate the weight of the mass. Give your answer to 2 significant figures.

b) Calculate the spring constant, \( k \), of the spring.

c) The student then replaces the mass with a different object, and the spring stores \( 0.25 \text{ J} \) of elastic potential energy. Calculate the extension of the spring produced by this object.