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Springs in Series

Part of the Mechanics section of Coddy's Physics journey. Lesson 58 of 97.

Two springs hooked end to end are in series. Both carry the same force, and their stretches add.

Two springs k1 and k2 hooked end to end below a ceiling, holding a block whose weight mg pulls down; the same force runs through both springs

In series: the same force runs through both springs.

The pair acts like one softer spring:

$\frac{1}{k} = \frac{1}{k_1} + \frac{1}{k_2}$

Two identical springs in series have half the spring constant of one.

Challenge

A $2\ \mathrm{kg}$ toy hangs at rest from two springs hooked end to end: a spring of $\relax k_{1}$ = $60\ \mathrm{N/m}$ on top and a second spring below it. Together the springs stretch $0.49\ \mathrm{m}$ . Find the spring constant $\relax k_{2}$ of the second spring.

Try it yourself

Physics diagram: spring, ball, path, crate

Solve for $k_{2}$

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Mechanics

1Introduction

What is Physics?Your First Equation Turning a Rule Around

4Inclined Planes

Forces on an Incline Gravity Components Frictionless Incline Incline with Friction Will It Slide?Recap - Ramp Challenge

7Projectile Motion

Independent Axes Horizontal Launch Launch at an Angle Range and Max Height Recap - Hit the Target

10Work and Energy

Work Kinetic Energy Work-Energy Theorem Gravitational PE Conservation of Energy Power Recap - Roller Coaster

13Impulse and Momentum

Momentum Impulse Conservation of Momentum Elastic Collisions Inelastic Collisions Recap - Air Track

16Simple Harmonic Motion

What is SHM?Mass on a Spring The Pendulum SHM Graphs Energy in SHM Recap - Oscillator

2Vectors and Newton's Laws

Right Triangles What is a Vector?Adding Vectors Axes and Directions Vector Components Forces Around Us Friction and Tension Newton's First Law Newton's Second Law Newton's Third Law Recap - Net Force

5Kinematics in 1D

Position and Displacement Velocity Acceleration Motion Graphs Equations of Motion Recap - Braking Car

8Kinematics and Newton

From Forces to Motion From Motion to Forces Two-Stage Motion Recap - Elevator

11Springs

Hooke's LawSprings in SeriesSprings in Parallel Recap - Spring Scale

14Momentum in 2D

Momentum as a Vector 2D Collisions Explosions Recap - Billiards

17Gravitation

Law of Gravitation Gravity and Altitude Satellites Kepler's Laws Gravitational Energy Escape Velocity Satellite Energy Recap - Mission to Orbit

3Friction

What is Friction?Static Friction Kinetic Friction Friction and Newton's Laws Recap - Sliding Crate

6Vertical Motion

Free Fall Throwing Upward Time in the Air Recap - Dropped Ball

9Project: Delivery Drone

Mission Briefing Takeoff Thrust Climb to Altitude Cruise and Brake Package Drop

12Elastic Energy

Elastic Potential Energy Spring Launchers Energy with Springs Recap - Spring Launcher

15Circular Motion

Uniform Circular Motion Centripetal Acceleration Horizontal Circles Vertical Circles Loop the Loop Recap - Car on a Curve

18Final Challenges

Recap - Stunt Ramp Recap - Crash Test Recap - Space Probe