AP Physics 1 Flashcards: Spring Forces

What this deck covers

This deck focuses on Spring Forces, giving you a quick way to review the definitions, rules, and examples that matter most for AP Physics 1.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Calculate potential energy for $k = 300 \, N/m$ and $x = 0.2 \, m$.

Answer: $U = 6 \, J$. Using $U = \frac{1}{2}kx^2 = \frac{1}{2}(300)(0.2)^2 = 6$ J.

Flashcard 2: State the formula for potential energy stored in a spring.

Answer: $U = \frac{1}{2}kx^2$. Energy stored when spring is displaced from equilibrium.

Flashcard 3: What happens to potential energy if displacement is tripled?

Answer: Increases ninefold. Potential energy depends on $x^2$, so $(3x)^2 = 9x^2$.

Flashcard 4: What type of motion does a mass undergo when attached to a spring?

Answer: Simple harmonic motion. Oscillatory motion with restoring force proportional to displacement.

Flashcard 5: What does the negative sign in Hooke's Law represent?

Answer: Opposite direction to displacement. Spring force always acts to restore equilibrium position.

Flashcard 6: Which physical law describes the force in a spring?

Answer: Hooke's Law. Named after Robert Hooke, describes elastic behavior.

Flashcard 7: What is the maximum force a spring can exert when fully stretched?

Answer: Force at maximum displacement. Occurs at maximum displacement from equilibrium.

Flashcard 8: What is the potential energy if $k = 100 \, N/m$ and $x = 0.1 \, m$?

Answer: $U = 0.5 \, J$. Using $U = \frac{1}{2}kx^2 = \frac{1}{2}(100)(0.1)^2 = 0.5$ J.

Flashcard 9: What is the restoring force in a spring system?

Answer: Force returning system to equilibrium. Force that opposes displacement from equilibrium.

Flashcard 10: Find the displacement if $F_s = -10 \, N$ and $k = 50 \, N/m$.

Answer: $x = 0.2 \, m$. From $x = \frac{F_s}{-k} = \frac{-10}{-50} = 0.2$ m.

Flashcard 11: Which physical law describes the force in a spring?

Answer: Hooke's Law. Named after Robert Hooke, describes elastic behavior.

Flashcard 12: Identify the unit of spring constant $k$ in SI units.

Answer: Newton per meter (N/m). Force per unit length, derived from $F = kx$.

Flashcard 13: Find the spring constant if $F_s = 50 \, N$ and $x = 0.25 \, m$.

Answer: $k = 200 \, N/m$. Using $k = \frac{F_s}{x} = \frac{50}{0.25} = 200$ N/m.

Flashcard 14: Calculate spring force with $k = 250 \, N/m$ and $x = -0.04 \, m$.

Answer: $F_s = 10 \, N$. Force magnitude: $|F_s| = k|x| = 250 \times 0.04 = 10$ N.

Flashcard 15: What does $k$ represent in Hooke's Law?

Answer: Spring constant. Measure of spring stiffness in Hooke's Law.

Flashcard 16: What is Hooke's Law formula for spring force?

Answer: $F_s = -kx$. The fundamental equation showing force is proportional to displacement.

Flashcard 17: Calculate the displacement if $F_s = -40 \, N$ and $k = 80 \, N/m$.

Answer: $x = 0.5 \, m$. Using $x = \frac{|F_s|}{k} = \frac{40}{80} = 0.5$ m.

Flashcard 18: What is the effect of increasing spring constant on stiffness?

Answer: Increases stiffness. Higher $k$ means greater resistance to deformation.

Flashcard 19: Identify the direction of spring force when a spring is compressed.

Answer: Opposite to compression. Spring pushes back against the compression direction.

Flashcard 20: What is the potential energy of a spring at maximum stretch?

Answer: Maximum potential energy. Energy is maximum when displacement is maximum.

Flashcard 21: Calculate spring force for $k = 100 \, N/m$ and $x = 0.05 \, m$.

Answer: $F_s = -5 \, N$. Using $F_s = -kx = -100 \times 0.05 = -5$ N.

Flashcard 22: Identify the proportionality constant in Hooke's Law.

Answer: Spring constant $k$. The coefficient relating force to displacement.

Flashcard 23: Find the spring constant when $U = 8 \, J$ and $x = 0.2 \, m$.

Answer: $k = 400 \, N/m$. From $k = \frac{2U}{x^2} = \frac{2(8)}{(0.2)^2} = 400$ N/m.

Flashcard 24: Find the spring force if $k = 200 \, N/m$ and $x = 0.1 \, m$.

Answer: $F_s = -20 \, N$. Using $F_s = -kx = -200 \times 0.1 = -20$ N.

Flashcard 25: What is the potential energy for a spring at its equilibrium position?

Answer: $0 \, J$. No displacement means no stored energy in the spring.

Flashcard 26: Identify the variable representing displacement in Hooke's Law.

Answer: $x$. Distance from equilibrium position, positive or negative.

Flashcard 27: Identify the proportionality constant in Hooke's Law.

Answer: Spring constant $k$. The coefficient relating force to displacement.

Flashcard 28: What is the unit of potential energy in the SI system?

Answer: Joule (J). Standard SI unit for all forms of energy.

Flashcard 29: What is the force exerted by a spring called?

Answer: Restoring force. Force that acts to restore system to equilibrium.

Flashcard 30: What type of motion does a mass undergo when attached to a spring?

Answer: Simple harmonic motion. Oscillatory motion with restoring force proportional to displacement.

Flashcard 31: Calculate the force if $k = 150 \, N/m$ and $x = -0.3 \, m$.

Answer: $F_s = 45 \, N$. Force magnitude: $|F_s| = kx = 150 \times 0.3 = 45$ N.

Flashcard 32: State the formula for potential energy stored in a spring.

Answer: $U = \frac{1}{2}kx^2$. Energy stored when spring is displaced from equilibrium.

Flashcard 33: What is the potential energy of a spring at maximum stretch?

Answer: Maximum potential energy. Energy is maximum when displacement is maximum.

Flashcard 34: What is the maximum force a spring can exert when fully stretched?

Answer: Force at maximum displacement. Occurs at maximum displacement from equilibrium.

Flashcard 35: What happens to spring force if the spring constant is doubled?

Answer: Force doubles. Force is directly proportional to spring constant.

Flashcard 36: Calculate spring force with $k = 250 \, N/m$ and $x = -0.04 \, m$.

Answer: $F_s = 10 \, N$. Force magnitude: $|F_s| = k|x| = 250 \times 0.04 = 10$ N.

Flashcard 37: What is the effect of increasing spring constant on stiffness?

Answer: Increases stiffness. Higher $k$ means greater resistance to deformation.

Flashcard 38: What is the restoring force in a spring system?

Answer: Force returning system to equilibrium. Force that opposes displacement from equilibrium.

Flashcard 39: What happens to potential energy if displacement is tripled?

Answer: Increases ninefold. Potential energy depends on $x^2$, so $(3x)^2 = 9x^2$.

Flashcard 40: Identify the variable representing potential energy in spring systems.

Answer: $U$. Symbol for potential energy in spring equations.

Flashcard 41: Identify the nature of the graph between force and displacement for springs.

Answer: Linear. Hooke's Law creates a straight-line relationship.

Flashcard 42: What is Hooke's Law formula for spring force?

Answer: $F_s = -kx$. The fundamental equation showing force is proportional to displacement.

Flashcard 43: Identify the type of force acting when a spring is neither compressed nor stretched.

Answer: No force (equilibrium). Spring is at its natural length with zero displacement.

Flashcard 44: What is the potential energy for a spring at its equilibrium position?

Answer: $0 \, J$. No displacement means no stored energy in the spring.

Flashcard 45: What does $k$ represent in Hooke's Law?

Answer: Spring constant. Measure of spring stiffness in Hooke's Law.

Flashcard 46: Calculate the force if $k = 150 \, N/m$ and $x = -0.3 \, m$.

Answer: $F_s = 45 \, N$. Force magnitude: $|F_s| = kx = 150 \times 0.3 = 45$ N.

Flashcard 47: Identify the variable representing potential energy in spring systems.

Answer: $U$. Symbol for potential energy in spring equations.

Flashcard 48: Determine potential energy if $k = 50 \, N/m$ and $x = 0.4 \, m$.

Answer: $U = 4 \, J$. Using $U = \frac{1}{2}kx^2 = \frac{1}{2}(50)(0.4)^2 = 4$ J.

Flashcard 49: Identify the type of force acting when a spring is neither compressed nor stretched.

Answer: No force (equilibrium). Spring is at its natural length with zero displacement.

Flashcard 50: Determine potential energy if $k = 50 \, N/m$ and $x = 0.4 \, m$.

Answer: $U = 4 \, J$. Using $U = \frac{1}{2}kx^2 = \frac{1}{2}(50)(0.4)^2 = 4$ J.

Flashcard 51: Find the spring constant for $F_s = 30 \, N$ and $x = 0.15 \, m$.

Answer: $k = 200 \, N/m$. From $k = \frac{F_s}{x} = \frac{30}{0.15} = 200$ N/m.

Flashcard 52: What is the equilibrium position of a spring?

Answer: Position where net force is zero. Natural length where spring exerts no force.

Flashcard 53: Identify the nature of the graph between force and displacement for springs.

Answer: Linear. Hooke's Law creates a straight-line relationship.

Flashcard 54: Find the displacement if $F_s = -10 \, N$ and $k = 50 \, N/m$.

Answer: $x = 0.2 \, m$. From $x = \frac{F_s}{-k} = \frac{-10}{-50} = 0.2$ m.

Flashcard 55: What is the equilibrium position of a spring?

Answer: Position where net force is zero. Natural length where spring exerts no force.

Flashcard 56: What is the potential energy at maximum compression for a spring?

Answer: Maximum potential energy. All kinetic energy converted to potential energy.

Flashcard 57: Find the spring constant for $F_s = 30 \, N$ and $x = 0.15 \, m$.

Answer: $k = 200 \, N/m$. From $k = \frac{F_s}{x} = \frac{30}{0.15} = 200$ N/m.

Flashcard 58: Find the spring force if $k = 200 \, N/m$ and $x = 0.1 \, m$.

Answer: $F_s = -20 \, N$. Using $F_s = -kx = -200 \times 0.1 = -20$ N.

Flashcard 59: What is the potential energy at maximum compression for a spring?

Answer: Maximum potential energy. All kinetic energy converted to potential energy.

Flashcard 60: Which type of energy is stored in a compressed or stretched spring?

Answer: Elastic potential energy. Energy stored due to elastic deformation of the spring.

Flashcard 61: Which type of energy is stored in a compressed or stretched spring?

Answer: Elastic potential energy. Energy stored due to elastic deformation of the spring.

Flashcard 62: Find the spring constant if $F_s = 50 \, N$ and $x = 0.25 \, m$.

Answer: $k = 200 \, N/m$. Using $k = \frac{F_s}{x} = \frac{50}{0.25} = 200$ N/m.

Flashcard 63: What is the unit of potential energy in the SI system?

Answer: Joule (J). Standard SI unit for all forms of energy.

Flashcard 64: What is the potential energy if $k = 100 \, N/m$ and $x = 0.1 \, m$?

Answer: $U = 0.5 \, J$. Using $U = \frac{1}{2}kx^2 = \frac{1}{2}(100)(0.1)^2 = 0.5$ J.

Flashcard 65: Identify the variable representing displacement in Hooke's Law.

Answer: $x$. Distance from equilibrium position, positive or negative.

Flashcard 66: What happens to spring force if the spring constant is doubled?

Answer: Force doubles. Force is directly proportional to spring constant.

Flashcard 67: Determine the spring constant if $U = 2 \, J$ and $x = 0.1 \, m$.

Answer: $k = 400 \, N/m$. From $k = \frac{2U}{x^2} = \frac{2(2)}{(0.1)^2} = 400$ N/m.

Flashcard 68: What does the negative sign in Hooke's Law represent?

Answer: Opposite direction to displacement. Spring force always acts to restore equilibrium position.

Flashcard 69: Calculate potential energy for $k = 300 \, N/m$ and $x = 0.2 \, m$.

Answer: $U = 6 \, J$. Using $U = \frac{1}{2}kx^2 = \frac{1}{2}(300)(0.2)^2 = 6$ J.

Flashcard 70: Identify the unit of spring constant $k$ in SI units.

Answer: Newton per meter (N/m). Force per unit length, derived from $F = kx$.

Flashcard 71: Calculate the displacement if $F_s = -40 \, N$ and $k = 80 \, N/m$.

Answer: $x = 0.5 \, m$. Using $x = \frac{|F_s|}{k} = \frac{40}{80} = 0.5$ m.

Flashcard 72: What is the relationship between spring force and displacement?

Answer: Directly proportional. Larger displacement produces proportionally larger force magnitude.

Flashcard 73: What is the relationship between spring force and displacement?

Answer: Directly proportional. Larger displacement produces proportionally larger force magnitude.

Flashcard 74: Find the spring constant when $U = 8 \, J$ and $x = 0.2 \, m$.

Answer: $k = 400 \, N/m$. From $k = \frac{2U}{x^2} = \frac{2(8)}{(0.2)^2} = 400$ N/m.

Flashcard 75: Identify the direction of spring force when a spring is compressed.

Answer: Opposite to compression. Spring pushes back against the compression direction.

Flashcard 76: Calculate spring force for $k = 100 \, N/m$ and $x = 0.05 \, m$.

Answer: $F_s = -5 \, N$. Using $F_s = -kx = -100 \times 0.05 = -5$ N.