In a theme park ride, a capsule of mass 180 kg is launched vertically upwards using two stretched elastic cords that behave like springs.
Before launch, each elastic cord is stretched by an extension of 8.0 m. The spring constant of each cord is 600 N/m. Calculate the total elastic potential energy stored in both cords combined before release. Use the equation:
elastic potential energy=0.5×spring constant×(extension)2 \text{elastic potential energy} = 0.5 \times \text{spring constant} \times (\text{extension})^2 elastic potential energy=0.5×spring constant×(extension)2At its maximum height, the capsule has 26,460 J26,460 \text{ J}26,460 J of gravitational potential energy. Calculate the maximum height reached by the capsule above its launch point. Use the equation:
gravitational potential energy=mass×gravitational field strength×height \text{gravitational potential energy} = \text{mass} \times \text{gravitational field strength} \times \text{height} gravitational potential energy=mass×gravitational field strength×heightTake the gravitational field strength as g=9.8 N/kgg = 9.8 \text{ N/kg}g=9.8 N/kg.
Explain why the maximum gravitational potential energy of the capsule is significantly less than the total initial elastic potential energy stored in the cords. State two reasons.