A.3 · IB Physics
Spring launcher and elastic energy
Compress a spring, release a block up a rough slope and watch elastic energy transfer into kinetic, gravitational and thermal stores.
E_el = ½kx²
½kx² = ½mv² + mg(sinθ + μcosθ)x
d = v² / (2g(sinθ + μcosθ))
g = 9.8 m s⁻²
Elastic energy:
Launch speed v:
Distance after launch d:
Total distance from release:
Height gained h:
Work against friction:
Try this
- Set μ = 0 and change x from 5 cm to 10 cm: check that the elastic energy and the total distance travelled both become four times larger.
- With μ = 0, run a launch and confirm that at the highest point the gravitational bar equals the initial ½kx²; then add friction and watch the thermal bar take a share.
- Set k = 100 N m⁻¹, m = 1.0 kg, x = 10 cm and μ = 0.2, then raise θ from 5° and find the angle (about 19°) at which the block no longer leaves the spring.
Exam tip: write a full energy balance, ½kx² = ½mv² + mgh + μmg cosθ·s, and remember that on a slope the height gained is h = s sinθ, not the distance s along the slope.