A vertical toy launcher uses two identical parallel springs to shoot a small dart vertically upwards.
At the lowest point, the extension of each of the two springs is 0.15 m0.15\text{ m}0.15 m. The spring constant of each spring is 60 N/m60\text{ N/m}60 N/m. Calculate the total elastic potential energy stored in the two springs.
As the launcher releases the dart, the springs return to their unstretched position. The kinetic energy of the dart at the point of release is less than the total elastic potential energy stored in the springs initially. Explain why.
In a second trial, the springs are stretched to a new position:
Calculate the maximum height reached by the dart above the release point. Assume all the initial elastic potential energy is converted to gravitational potential energy when the dart is at its maximum height. Use the equation: potential energy=mass×gravitational field strength×height\text{potential energy} = \text{mass} \times \text{gravitational field strength} \times \text{height}potential energy=mass×gravitational field strength×height (Take the gravitational field strength g=10 N/kgg = 10\text{ N/kg}g=10 N/kg.)
A student investigates how the mass of the dart affects its launch speed at release. Describe one factor the student must control in this investigation.