## PhET Tutorial: Masses & Springs

**Learning Goal: **To understand how the motion and energetics of a weight attached to a vertical spring depend on the mass, the spring constant, and initial conditions.

For this tutorial, use the PhET simulation *Masses & Springs*. You can put a weight on the end of a hanging spring, stretch the spring, and watch the resulting motion.

A) **Place a ****50 ****weight on spring #1, and release it. Eventually, the weight will come to rest at an equilibrium position, with the spring somewhat stretched compared to its original (unweighted) length. At this point, the upward force of the spring balances the force of gravity on the weight.**

**With the weight in its equilibrium position, how does the amount the spring is stretched depend on the mass of the weight?**

**B) Use the simulation to estimate the masses of the three colored, unlabeled weights. Then, place them into the appropriate mass bins.**

**C) Recall that in the equilibrium position, the upward force of the spring balances the force of gravity on the weight. Use this concept to estimate the spring constant of spring #1.**

**D) Now, for parts D-F, you’ll investigate the energetics of the spring.****Select ****1**** in the ****Show Energy of**** box, which shows an energy bar diagram. Select the ****g = 0**** option (under the planet names), which simulates what happens without any gravitational forces (and consequently removes gravitational potential energy from the energetics). Adjust the****friction**** slider to ****none**** (this prevents any thermal energy from being generated). Place a weight on spring #1, stretch it, and release it. Watch how the kinetic energy and elastic potential energy vary with time. (You can slow down or stop time using the buttons next to the list of planets.)**

**When is the elastic potential energy of the spring a maximum?**

**E) When is the kinetic energy of the mass a maximum?**

**F) Select ****Earth**** in the menu box so that there is now a force of gravity. Now the total energy of the mass/spring system is the sum of the kinetic energy, the elastic potential energy, and the gravitational potential energy.**

**When is the kinetic energy a maximum? (It may help to watch the simulation in slow motion – 1/16 time.)**

**G) Now, for parts G-I, you’ll investigate what determines the frequency of oscillation. For these parts, turn off the friction using the slider bar.**

**Select the stopwatch, and time how long it takes for a weight to oscillate back and forth 10 times. The period of oscillation is this time divided by 10. The frequency of oscillation is one divided by the period.**

**How does the frequency of oscillation depend on the mass of the weight?**

**H) The amplitude of oscillation is the maximum distance between the oscillating weight and the equilibrium position. Determine the frequency of oscillation for several different amplitudes by pulling the weight down different amounts.****How does the frequency depend on the amplitude of oscillation?**

**I) The spring constant of spring #3 can be adjusted with the ****softness spring 3**** slider bar (harder means a greater spring constant, or stiffer spring).**

**How does the frequency of oscillation depend on the spring constant?**

## Answer ( 1 )

A)

=> The spring stretches more for a heavier weight

B)=>

C)=> k = 10 N/M

D)=> Both when the spring is most compressed and when the spring is most stretched

E)=> When the spring is at its unweighted length (when it isn’t stretched or compressed)

F)=> When the mass is at the equilibrium position

G)=> The frequency decreases as the mass increases

H)=> The frequency is independent of the amplitude.

I)=> The frequency increases as the spring constant increases