Rides and rollercoasters
Many theme park rides use the transfer of gravitational potential energy to kinetic energy and kinetic energy to gravitational potential energy.
A rollercoaster car converts GPE to KE when it rolls down the track As the pirate ship falls, GPE is transferred into KE. At the bottom of the swing it's travelling at its highest speed. As it swings back up the other side it slows down as its KE is transferred back into GPE. Rollercoasters use these energy transfers too.
The rollercoaster car gains GPE as it travels to the top. Once over the top, the car gains speed as GPE is transferred to KE. As it travels to the top of another loop, KE is transferred to GPE. Note that not all the energy is transferred to or from GPE – some is transferred to the surroundings as heat and sound. Remember that all moving objects have kinetic energy, KE. The kinetic energy an object has depends on its: Mass – if the mass doubles, the KE doubles
Speed – if the speed doubles, the KE quadruples (increases four times). When an object falls through the atmosphere at terminal speed: its kinetic energy, KE, does not increase
gravitational potential energy, GPE is transferred to the surroundings as heat because of friction (air resistance). Remember that:
GPE = mgh
KE = ½ mv2
Assuming that all the gravitational potential energy of a falling object is transferred to kinetic energy: GPE = KE
… so …
mgh = ½ mv2
Notice that m appears on both sides of the equation and can be cancelled out: gh = ½ v2
This equation can be rearranged to give:
h = v2 ÷ 2g
For example, how high must an object be dropped so that is reaches 30 m/s? (g = 10 N/kg) height = 302 ÷ (2 × 10) = 900 ÷ 20 = 45 m
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