A spring with a spring constant of 3200 N / m is initially stretched until the elastic potentia

step 1 So here, for Part A, we're going to use equation 811 in order to find the initial elongation, th

A spring with a spring constant of 3200 N / m is initially...

A spring with a spring constant of $3200 \mathrm{~N} / \mathrm{m}$ is initially stretched until the elastic potential energy of the spring is $1.44 \mathrm{~J} .$ $(U=0$ for the relaxed spring.) What is $\Delta U$ if the initial stretch is changed to (a) a stretch of $2.0 \mathrm{~cm},(\mathrm{~b})$ a compression of $2.0 \mathrm{~cm}$, and (c) a compression of $4.0 \mathrm{~cm}$ ?

Key Concepts

Hooke's Law

Hooke's Law is a principle of physics that states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position. This law is typically expressed as F = -kx, where F is the restoring force, k is the spring constant, and x is the displacement. It provides the foundational understanding for analyzing how springs behave under stretching or compression.

Elastic Potential Energy

Elastic potential energy refers to the energy stored in an elastic object when it is deformed, such as when a spring is stretched or compressed. The energy stored in a spring is given by the formula U = (1/2)kx², where k is the spring constant and x is the displacement from the spring’s relaxed length. This concept is essential for understanding energy storage and release in elastic systems.

Spring Constant

The spring constant, denoted by k, is a measure of the stiffness of a spring and quantifies the relationship between the force applied and the displacement produced. A larger spring constant indicates a stiffer spring that requires more force to achieve the same displacement as compared to a spring with a lower spring constant. This parameter is crucial in quantifying the energy and forces involved in spring systems.

Displacement in Springs

Displacement in springs refers to the distance and direction by which a spring is stretched or compressed relative to its equilibrium (relaxed) position. This displacement, when substituted into the elastic potential energy equation, determines the amount of energy stored within the spring. Whether the displacement is positive (stretching) or negative (compression), the energy stored depends on the square of the displacement, making the effect symmetric in magnitude.

Transcript

Please give Ace some feedback