- #1
- 19,854
- 10,836
Definition/Summary
A spring is a mechanical device that produces a restoring force when stretched or compressed. The restoring force acts to restore the spring to its equilibrium position, and is typically proportional to displacement.
Similarly, a torsion spring produces a restoring torque when twisted.
Equations
<br /> \begin{align*}<br /> & F = -k x \ \ \ \ \ \ \text{(Hooke's Law)} \\ <br /> & \\<br /> & T = -k \theta \ \ \ \ \ \ \text{(Torsion spring)} \\ <br /> & \\<br /> & U = \frac{1}{2} k x^2 \ \text{or} \ \frac{1}{2} k \theta^2 <br /> \ \ \ \ \ \ \text{(Potential energy)} \\ <br /> & \\<br /> & k_{net} = k_1 + k_2 \ \ \ \ \ \ \text{(combining 2 springs in parallel)} \\<br /> & \\<br /> & \frac{1}{k_{net}} = \frac{1}{k_1} + \frac{1}{k_2} \ \ \ \ \ \ \text{(combining 2 springs in series)} \\<br /> \end{align*}<br />
Extended explanation
Definition of terms
Angle units for torsion springs
* This entry is from our old Library feature, and was originally created by Redbelly98
A spring is a mechanical device that produces a restoring force when stretched or compressed. The restoring force acts to restore the spring to its equilibrium position, and is typically proportional to displacement.
Similarly, a torsion spring produces a restoring torque when twisted.
Equations
<br /> \begin{align*}<br /> & F = -k x \ \ \ \ \ \ \text{(Hooke's Law)} \\ <br /> & \\<br /> & T = -k \theta \ \ \ \ \ \ \text{(Torsion spring)} \\ <br /> & \\<br /> & U = \frac{1}{2} k x^2 \ \text{or} \ \frac{1}{2} k \theta^2 <br /> \ \ \ \ \ \ \text{(Potential energy)} \\ <br /> & \\<br /> & k_{net} = k_1 + k_2 \ \ \ \ \ \ \text{(combining 2 springs in parallel)} \\<br /> & \\<br /> & \frac{1}{k_{net}} = \frac{1}{k_1} + \frac{1}{k_2} \ \ \ \ \ \ \text{(combining 2 springs in series)} \\<br /> \end{align*}<br />
Extended explanation
Definition of terms
Hooke's Law:
F is the force exerted by the spring on an object attached to it.
x is the spring's displacement from it's equilibrium length.
k is the spring constant, with SI units of N/m.
Torsion spring:
T is the torque exerted by the spring on an object attached to it.
θ is the spring's angular displacement from it's equilibrium position.
k is the spring constant, with SI units of N-m / rad.
U is the potential energy stored in the spring.
k1 and k2 are the spring constants of two separate springs
knet is the net or effective spring constant for two springs attached to each other.
F is the force exerted by the spring on an object attached to it.
x is the spring's displacement from it's equilibrium length.
k is the spring constant, with SI units of N/m.
Torsion spring:
T is the torque exerted by the spring on an object attached to it.
θ is the spring's angular displacement from it's equilibrium position.
k is the spring constant, with SI units of N-m / rad.
U is the potential energy stored in the spring.
k1 and k2 are the spring constants of two separate springs
knet is the net or effective spring constant for two springs attached to each other.
Angle units for torsion springs
To use the potential energy equation, the angle and spring constant must be in terms of radians.
To use the torsion spring equation for torque, the angle and spring constant may be in terms of any angular units (such as degrees).
To calculate energy when the spring constant is given in terms of degrees, either convert k to be in terms of radians, or use the rather unwieldy form
To use the torsion spring equation for torque, the angle and spring constant may be in terms of any angular units (such as degrees).
To calculate energy when the spring constant is given in terms of degrees, either convert k to be in terms of radians, or use the rather unwieldy form
U = ½ k (θ in degrees) (θ in radians)
* This entry is from our old Library feature, and was originally created by Redbelly98
Last edited by a moderator: