Spring Forces - AP Physics 1
Card 1 of 30
Which physical law describes the force in a spring?
Which physical law describes the force in a spring?
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Hooke's Law. Named after Robert Hooke, describes elastic behavior.
Hooke's Law. Named after Robert Hooke, describes elastic behavior.
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Find the spring constant if $F_s = 50 , N$ and $x = 0.25 , m$.
Find the spring constant if $F_s = 50 , N$ and $x = 0.25 , m$.
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$k = 200 , N/m$. Using $k = \frac{F_s}{x} = \frac{50}{0.25} = 200$ N/m.
$k = 200 , N/m$. Using $k = \frac{F_s}{x} = \frac{50}{0.25} = 200$ N/m.
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State the formula for potential energy stored in a spring.
State the formula for potential energy stored in a spring.
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$U = \frac{1}{2}kx^2$. Energy stored when spring is displaced from equilibrium.
$U = \frac{1}{2}kx^2$. Energy stored when spring is displaced from equilibrium.
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Find the displacement if $F_s = -10 , N$ and $k = 50 , N/m$.
Find the displacement if $F_s = -10 , N$ and $k = 50 , N/m$.
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$x = 0.2 , m$. From $x = \frac{F_s}{-k} = \frac{-10}{-50} = 0.2$ m.
$x = 0.2 , m$. From $x = \frac{F_s}{-k} = \frac{-10}{-50} = 0.2$ m.
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Identify the proportionality constant in Hooke's Law.
Identify the proportionality constant in Hooke's Law.
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Spring constant $k$. The coefficient relating force to displacement.
Spring constant $k$. The coefficient relating force to displacement.
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Determine potential energy if $k = 50 , N/m$ and $x = 0.4 , m$.
Determine potential energy if $k = 50 , N/m$ and $x = 0.4 , m$.
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$U = 4 , J$. Using $U = \frac{1}{2}kx^2 = \frac{1}{2}(50)(0.4)^2 = 4$ J.
$U = 4 , J$. Using $U = \frac{1}{2}kx^2 = \frac{1}{2}(50)(0.4)^2 = 4$ J.
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What is the relationship between spring force and displacement?
What is the relationship between spring force and displacement?
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Directly proportional. Larger displacement produces proportionally larger force magnitude.
Directly proportional. Larger displacement produces proportionally larger force magnitude.
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What is the potential energy for a spring at its equilibrium position?
What is the potential energy for a spring at its equilibrium position?
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$0 , J$. No displacement means no stored energy in the spring.
$0 , J$. No displacement means no stored energy in the spring.
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Identify the type of force acting when a spring is neither compressed nor stretched.
Identify the type of force acting when a spring is neither compressed nor stretched.
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No force (equilibrium). Spring is at its natural length with zero displacement.
No force (equilibrium). Spring is at its natural length with zero displacement.
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Find the spring constant for $F_s = 30 , N$ and $x = 0.15 , m$.
Find the spring constant for $F_s = 30 , N$ and $x = 0.15 , m$.
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$k = 200 , N/m$. From $k = \frac{F_s}{x} = \frac{30}{0.15} = 200$ N/m.
$k = 200 , N/m$. From $k = \frac{F_s}{x} = \frac{30}{0.15} = 200$ N/m.
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Identify the direction of spring force when a spring is compressed.
Identify the direction of spring force when a spring is compressed.
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Opposite to compression. Spring pushes back against the compression direction.
Opposite to compression. Spring pushes back against the compression direction.
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What is the restoring force in a spring system?
What is the restoring force in a spring system?
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Force returning system to equilibrium. Force that opposes displacement from equilibrium.
Force returning system to equilibrium. Force that opposes displacement from equilibrium.
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What happens to spring force if the spring constant is doubled?
What happens to spring force if the spring constant is doubled?
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Force doubles. Force is directly proportional to spring constant.
Force doubles. Force is directly proportional to spring constant.
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What is the potential energy if $k = 100 , N/m$ and $x = 0.1 , m$?
What is the potential energy if $k = 100 , N/m$ and $x = 0.1 , m$?
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$U = 0.5 , J$. Using $U = \frac{1}{2}kx^2 = \frac{1}{2}(100)(0.1)^2 = 0.5$ J.
$U = 0.5 , J$. Using $U = \frac{1}{2}kx^2 = \frac{1}{2}(100)(0.1)^2 = 0.5$ J.
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What is the equilibrium position of a spring?
What is the equilibrium position of a spring?
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Position where net force is zero. Natural length where spring exerts no force.
Position where net force is zero. Natural length where spring exerts no force.
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Identify the unit of spring constant $k$ in SI units.
Identify the unit of spring constant $k$ in SI units.
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Newton per meter (N/m). Force per unit length, derived from $F = kx$.
Newton per meter (N/m). Force per unit length, derived from $F = kx$.
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What is the unit of potential energy in the SI system?
What is the unit of potential energy in the SI system?
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Joule (J). Standard SI unit for all forms of energy.
Joule (J). Standard SI unit for all forms of energy.
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Identify the proportionality constant in Hooke's Law.
Identify the proportionality constant in Hooke's Law.
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Spring constant $k$. The coefficient relating force to displacement.
Spring constant $k$. The coefficient relating force to displacement.
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Calculate the force if $k = 150 , N/m$ and $x = -0.3 , m$.
Calculate the force if $k = 150 , N/m$ and $x = -0.3 , m$.
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$F_s = 45 , N$. Force magnitude: $|F_s| = kx = 150 \times 0.3 = 45$ N.
$F_s = 45 , N$. Force magnitude: $|F_s| = kx = 150 \times 0.3 = 45$ N.
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What is the potential energy of a spring at maximum stretch?
What is the potential energy of a spring at maximum stretch?
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Maximum potential energy. Energy is maximum when displacement is maximum.
Maximum potential energy. Energy is maximum when displacement is maximum.
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Calculate spring force with $k = 250 , N/m$ and $x = -0.04 , m$.
Calculate spring force with $k = 250 , N/m$ and $x = -0.04 , m$.
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$F_s = 10 , N$. Force magnitude: $|F_s| = k|x| = 250 \times 0.04 = 10$ N.
$F_s = 10 , N$. Force magnitude: $|F_s| = k|x| = 250 \times 0.04 = 10$ N.
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What type of motion does a mass undergo when attached to a spring?
What type of motion does a mass undergo when attached to a spring?
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Simple harmonic motion. Oscillatory motion with restoring force proportional to displacement.
Simple harmonic motion. Oscillatory motion with restoring force proportional to displacement.
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What happens to potential energy if displacement is tripled?
What happens to potential energy if displacement is tripled?
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Increases ninefold. Potential energy depends on $x^2$, so $(3x)^2 = 9x^2$.
Increases ninefold. Potential energy depends on $x^2$, so $(3x)^2 = 9x^2$.
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What is the potential energy for a spring at its equilibrium position?
What is the potential energy for a spring at its equilibrium position?
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$0 , J$. No displacement means no stored energy in the spring.
$0 , J$. No displacement means no stored energy in the spring.
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Identify the variable representing potential energy in spring systems.
Identify the variable representing potential energy in spring systems.
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$U$. Symbol for potential energy in spring equations.
$U$. Symbol for potential energy in spring equations.
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Find the spring force if $k = 200 , N/m$ and $x = 0.1 , m$.
Find the spring force if $k = 200 , N/m$ and $x = 0.1 , m$.
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$F_s = -20 , N$. Using $F_s = -kx = -200 \times 0.1 = -20$ N.
$F_s = -20 , N$. Using $F_s = -kx = -200 \times 0.1 = -20$ N.
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Identify the type of force acting when a spring is neither compressed nor stretched.
Identify the type of force acting when a spring is neither compressed nor stretched.
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No force (equilibrium). Spring is at its natural length with zero displacement.
No force (equilibrium). Spring is at its natural length with zero displacement.
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Find the spring constant for $F_s = 30 , N$ and $x = 0.15 , m$.
Find the spring constant for $F_s = 30 , N$ and $x = 0.15 , m$.
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$k = 200 , N/m$. From $k = \frac{F_s}{x} = \frac{30}{0.15} = 200$ N/m.
$k = 200 , N/m$. From $k = \frac{F_s}{x} = \frac{30}{0.15} = 200$ N/m.
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Identify the variable representing displacement in Hooke's Law.
Identify the variable representing displacement in Hooke's Law.
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$x$. Distance from equilibrium position, positive or negative.
$x$. Distance from equilibrium position, positive or negative.
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What is the maximum force a spring can exert when fully stretched?
What is the maximum force a spring can exert when fully stretched?
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Force at maximum displacement. Occurs at maximum displacement from equilibrium.
Force at maximum displacement. Occurs at maximum displacement from equilibrium.
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