2.8 Spring Forces

• What are spring forces exerted by a spring when it is compressed or stretched from its equilibrium position?

  Compression or tension forces
• What is the formula for Hooke's Law?

  $F =$$- kx$
• The negative sign in Hooke's Law indicates that the spring force acts in the opposite direction to the displacement.
• A higher spring constant indicates a stiffer spring.

  True
• Arrange the following states of a spring based on its length relative to equilibrium:

  1️⃣ Compressed

  2️⃣ Equilibrium

  3️⃣ Stretched
• What are the three possible orientations of a spring?

  Vertical, horizontal, angled
• Each orientation of a spring affects its force and components.

  True
• A horizontal spring exerts force along a flat surface
• What is Hooke's Law in equation form?

  $F =$$- kx$
• What does the spring constant $k$ measure?


  Stiffness
• If a spring with $k =$$100 \text{ N / m}$ is stretched $x =$$0.2 \text{ m}$, the spring force is -20 N.
• Why is the negative sign included in Hooke's Law?

  To show restoring force
• What does a higher spring constant $k$ indicate?


  A stiffer spring
• If a spring requires 50 N of force to stretch 0.1 meters, its spring constant is 500 N/m.
• The equilibrium length is the reference point for measuring displacement in Hooke's Law.


  True
• How does the orientation of a spring affect its force?

  Magnitude and direction
• What does the negative sign in Hooke's Law indicate about the direction of the spring force?

  Opposite to displacement
• Hooke's Law describes the magnitude of the spring force when a spring is either compressed or stretched from its equilibrium position.


  True
• Match the variable with its description and units:

  $F$ ↔️ Magnitude of the spring force in Newtons (N)

  $k$ ↔️ Spring constant in N/m

  $x$ ↔️ Displacement from equilibrium in meters (m)
• The orientation of a spring affects the forces it exerts.


  True
• A spring with a spring constant $k =$$100 \text{ N / m}$ is stretched by $x =$$0.2 \text{ m}$. The force exerted by the spring is -20 N.
• The negative sign in Hooke's Law indicates that the spring force acts in the opposite direction to the displacement.
• When a mass is attached to a spring, the spring force acts to restore it to its equilibrium position.
• In a spring system, the spring force is often the only force acting on the mass if friction is ignored.


  True
• A mass of $2 \text{ kg}$ is attached to a spring with $k =$$50 \text{ N / m}$ and stretched $0.1 \text{ m}$ from equilibrium. What is the acceleration of the mass?


  $- 2.5 \text{ m / s}^{2}$
• The magnitude of the spring force is described by Hooke's Law.
• Match the variables in Hooke's Law with their descriptions and units:

  F ↔️ Magnitude of the spring force, Newtons (N)

  k ↔️ Spring constant (stiffness), N/m

  x ↔️ Displacement from equilibrium, meters (m)
• What is the spring force exerted by a spring with $k =$$100 \text{ N / m}$ when stretched by $x =$$0.2 \text{ m}$?


  $- 20 \text{ N}$
• What is the spring constant of a spring that requires 50 N of force to stretch 0.1 meters?

  $500 \text{ N / m}$
• Match the spring orientation with its example:

  Vertical ↔️ Supporting a weight

  Horizontal ↔️ Pulling a sled

  Angled ↔️ Supporting weight while pulling forward
• Angled springs exert force components in both vertical and horizontal
• What is an example of a vertical spring in use?

  Supporting a plant pot
• An angled spring has both vertical and horizontal components of force.


  True
• The unit of the spring force, $F$, is Newtons
• The negative sign in Hooke's Law indicates the spring force acts in the opposite direction to the displacement.


  True
• What does Hooke's Law describe in relation to springs?

  Force and displacement
• If a spring with $k =$$400 \text{ N / m}$ is stretched by $x =$$0.05 \text{ m}$, the spring force is -20 N.
• The units of the spring constant $k$ are Newtons per meter (N/m).


  True
• What is the equilibrium length of a spring?

  Natural length when unstretched
• A spring with an equilibrium length of 20 cm is compressed to 15 cm. The displacement is -5 cm.