Straight Up, On the Rocks

EF 151

Marie Pierce

Brittany Kopcsak

Michael Love

Alaka Hoskins

Overview & Design Construction:

The task given was to create a “motor” that would lift a mass of one kilogram to a height of one meter in as close to ten seconds as possible. Initially, we had no idea what or how we were going to accomplish this. Many ideas such as the slow release of water or sand to raise the weight were tossed around, but eventually discarded upon further consideration. We looked over many examples and brainstormed several ideas of ways to transfer energy. These ideas included creating a Newton’s Cradle with several elastic collisions, using ramps for gravitational potential to kinetic energy transfers, and using the elastic potential energy of a mousetrap’s spring to create more kinetic energy. Finally, we had some ideas and we went to Walmart to get the supplies. Being on a budget, we had to get materials we knew would not be very sturdy in the long run such as Styrofoam, and foam paper. At last, we returned to school with our materials and our ideas and began construction. The initial step was the Newton’s Cradle which we made by screwing eye-hole screws in the top of four golf balls, suspending them from string tied to two dowel rods. We attached this to a piece of foam board glued perpendicularly to a thick Styrofoam base. The next step was to place the last golf ball on a ramp strategically to where the Newton’s Cradle (when activated) will hit it down the ramp. At the end of the first Styrofoam ramp, the golf ball taps the end of a funnel containing a makeshift olive which then falls into a Martini glass below and creates some energy losses in the ball’s kinetic energy. The golf ball continues down two more ramps only to hit a mousetrap resting below the Martini glass. The tight spring constant provided by the mousetrap flips the glass with the olive and some clear marbles made to look like ice into a bucket below. The bucket is attached to a pulley system and is already at impending motion with the one kilogram mass due to the amount of sand it contains. The force of the added weight hitting the bucket pushes it down while simultaneously lifting the mass.

Stored Energy:

Golf ball mass = 0.045 kg

A

1.mgh = ½ mvA2 + mgh

(9.81 m/s2)(2921 m) = ½ vA2 + (9.81 m/s2)(.269875 m)

vA = .66034 m/s

The first step is a series of perfectly elastic collisions. We pull back on the first

ball creating potential energy which is converted to kinetic energy when released. This kinetic energy travels through each ball until it hits the ball sitting on ramp giving it an initial velocity of .66 m/s.

2.½ mvA2 + mgh = ½ mvB2 + mgh

½(.66034 m/s)2 + (9.81 m/s2)(.269875 m) = ½vB2 + (9.81 m/s2)(.254 m)

vB = 0.8646 m/s

The ball gains momentum as it rolls down the ramp and therefore has

a velocity of 0.86 m/s at the end of the ramp.

3.½ mvB2 + mgh = ½ mvC2 + mgh

½(.8646 m/s)2 + (9.81 m/s2)(.254 m) = ½vC2 + (9.81 m/s2)(.1778 m)

vC = 1.498 m/s

When the balls comes to the end of the ramp, it gains potential energy as is falls to

the top of the second ramp where its velocity is 1.498 m/s.

4. ½ mvC2 + mgh = ½ mvD2 + mgh

½(1.498 m/s)2 + (9.81 m/s2)(.1778 m) = ½vD2 + (9.81 m/s2)(.1524 m)

vD = 1.656 m/s

The ball gains momentum as it rolls down the second ramp, therefore its velocity

at the end of the ramp is 1.656 m/s.

5.½ mvD2 + mgh = ½ mvE2 + mgh

½(1.656 m/s)2 + (9.81 m/s2)(.1524 m) = ½vE2 + (9.81 m/s2)(.0889 m)

vE = 1.997 m/s

When the ball reaches the end of the second ramp, it gains potential energy as it

falls to the top of the third ramp where its velocity is 1.997 m/s.

6. ½ mvE2 + mgh = ½ mvF2 + mgh

½(1.997 m/s)2 + (9.81 m/s2)(.0889 m) = ½vF2 + (9.81 m/s2)(.0635 m)

vF = 2.118 m/s

The ball gains momentum as it rolls down the third ramp, when it reaches the end

its velocity is 2.118 m/s.

7. 1 in. Range = (vF2 / g) sin2Θ

12 in.Range = 2.118 m/s (sin 2(4.78))

4.78 degrees 9.81 m/s2

Range = 0.0359 m or 1.41 in.

When the ball rolls off the end of the third ramp it’s velocity allows it to travel a distance of 1.41 inches horizontally before it hits the foam base.

8.½ mvF2 + mgh = ½ mvG2

½(2.118 m/s)2 + (9.81 m/s2)(0.635 m) = ½vG2

vG = 2.39 m/s

When the ball rolls off the end of the third ramp, it also gains potential energy and

it's velocity right before it hits the ground is 2.39 m/s.

9.e = -vA2 + vB2= h2 => -vH = h2

vA1 – vB1 h1 vG h1

-vH = 0.5 in.

2.118 m/s 2.5 in.

vH = .4236 m/s

The ball then hits the ground and after it bounces back up it’s velocity is .4236 m/s as it hits the mousetrap trigger.

Bill of Materials:

  • Styrofoam base: $2
  • Foam paper: $0.50
  • Foam board: $1
  • String: $1
  • Dowel rods and wood: $2
  • Mousetraps: 4 for $1
  • Martini glass: $2
  • Bucket: $1
  • Golf balls: $4
  • Screws: $0.50
  • Glue: $2
  • Funnel: $1
  • Crafts for Olive: $1
  • Marbles: $1

Total: $20

Conclusion:

Over the course of constructing the aforementioned design, we ran into many complications, set backs, and problems. Our most prevalent problem we encountered throughout the entire project was the issue of stability with our materials. Due to our rather low budget, we could not buy the optimal materials. The foam board background needed many supports and braces on the back. The more we added to the project, the more pieces of wood for which we had to scavenge. When the project was finally completed, we were testing what we thought to be the final product and realized we had complications with the mass catching on the side of our bucket. In order to fix this, we had to construct an arm that would defer the bucket from its original path. Again, we faced the stability issue; also, the addition of this wooden bar added a great amount of friction to the string. There were a few problems with the golf ball getting caught between the ramp and the funnel (we had to make a groove between the two for it to fit), with the ball missing the mousetrap (we added a wooden wedge to direct it), and with the ball falling off of the ramps (we attached a foam piece to the edge to act as a wall). The Styrofoam base ended up coming in handy because we could easily add anything to the project simply by sticking it into the foam. When it came down to the presentation, all went well. The only slight problem we could not get rid of was the friction in the arm bar. This required a few taps on the weight and it continued upward.