Sled Energy and Collisions

1. Choose Bear at the bottom or Both bears on hills at the top of the picture.
2. Set where the red bear is released: move its Release height slider, type a height in the box, or drag the sled up or down the hill. The release height can be 0 to 50 m. Its Height also shows in the bottom corner. A higher start means a faster bear at the bottom.
3. Set each bear's mass with its slider, or type a number in the box. The mass can be 10 to 200 kg. A bear with more mass looks bigger.
4. With both bears on hills, set the blue bear's release height too, and choose Sleds stick together or Sleds bounce.
5. Check Show energy to see each bear's potential energy and kinetic energy while it moves.
6. Press Play (the triangle). The speed gauges show how fast each bear is going.
7. With the bear at the bottom, watch the blue bear slide along the measuring tape. When it stops, the Collision result box shows what happened, and the run is saved in the Data table under the picture: the red bear's speed at the bottom, its kinetic energy, and how far the blue bear slid.
8. Press Pause to freeze the action. Press Reset to put the bears back. You must reset before you can change the setup.
9. Copy data copies the table so you can paste it into a spreadsheet. Delete last run takes back one run. Clear table starts over (click it twice).

Potential energy (PE) is stored energy. Here it comes from height. A bear high on the hill has a lot of it. More height or more mass means more potential energy.

Kinetic energy (KE) is the energy of motion. A faster bear has more kinetic energy. So does a heavier bear going the same speed.

As the red bear slides down, its potential energy changes into kinetic energy. At the bottom, all of it is kinetic energy. The hill and the ice have no friction, so the total energy stays the same the whole way down.

The speed at the bottom depends only on the height. A 50 kg bear and a 200 kg bear that start at 10 m both reach 14 m/s. The heavier bear has more energy, though.

When the red bear hits the blue bear, it gives the blue bear its kinetic energy. This is an energy transfer. If the two bears have the same mass, the red bear stops dead and the blue bear takes all of its energy and speed. A heavier red bear keeps a little energy and keeps rolling slowly. A lighter red bear bounces back.

Past the start line the snow is rough. Friction slows the blue bear down and turns its kinetic energy into thermal energy (heat). The more kinetic energy the blue bear gets, the farther it slides before it stops.

Speed counts more than mass. Twice the mass gives twice the kinetic energy. Twice the speed gives four times the kinetic energy, so the blue bear slides about four times as far.

Momentum is mass times velocity. Velocity is speed in a direction. Here, moving right counts as plus and moving left counts as minus.

When the sleds crash, the total momentum before the crash equals the total momentum after it. This is called conservation of momentum.

Sleds stick together: the sleds move as one after the crash. Some kinetic energy turns into heat and sound, so there is less kinetic energy after the crash. Two sleds with the same mass and speed stop dead.

Sleds bounce: the sleds push off each other like springs. No kinetic energy is lost. A light sled hit by a heavy sled can fly away fast, even over the top of the hill.

• Potential energy: PE = m × g × h
• Kinetic energy: KE = ½ × m × v²
• Use m in kilograms, h in meters, v in meters per second, and g = 9.8 N/kg. Then the energy comes out in joules (J).
• Speed at the bottom of the hill (no friction): v = √(2 × g × h)
• Momentum: p = m × v
• Bear at the bottom: the sleds bounce. The blue bear's speed after the hit is v₂ = 2 × m₁ × v₁ ÷ (m₁ + m₂). With equal masses, that is the red bear's whole speed.
• Friction on the rough snow slows a bear by 4.9 m/s every second. Distance it slides: d = v² ÷ 9.8 (d in meters, v in m/s).
• Sleds stick together: v = (m₁v₁ + m₂v₂) ÷ (m₁ + m₂)
• Sleds bounce: the total kinetic energy after the crash equals the total before it.