This question is about energy transfers. A roller coaster cart with a mass of 600 kg600\text{ kg}600 kg rolls down a track with its motor switched off.
The track height is 20 m20\text{ m}20 m. The gravitational field strength is 10 N/kg10\text{ N/kg}10 N/kg. Calculate the potential energy of the cart at the top of the track. Use the equation: potential energy=mass×height×gravitational field strength\text{potential energy} = \text{mass} \times \text{height} \times \text{gravitational field strength}potential energy=mass×height×gravitational field strength.
The speed of the cart at the bottom of the track is 15 m/s15\text{ m/s}15 m/s. Calculate the kinetic energy of the cart at the bottom of the track. Use the equation: kinetic energy=12×mass×(speed)2\text{kinetic energy} = \frac{1}{2} \times \text{mass} \times (\text{speed})^2kinetic energy=21×mass×(speed)2.
The kinetic energy at the bottom of the track is less than the potential energy at the top of the track. Explain why. Write about energy stores.
The test is repeated with a different roller coaster cart. The potential energy of this cart at the top of the track is 150 000 J150\,000\text{ J}150000 J. The kinetic energy of this cart at the bottom of the track is 105 000 J105\,000\text{ J}105000 J. Calculate the efficiency of the transfer of energy from the potential store to the kinetic store. Use the equation: efficiency=useful output energy transferinput energy transfer\text{efficiency} = \frac{\text{useful output energy transfer}}{\text{input energy transfer}}efficiency=input energy transferuseful output energy transfer.