Question
The 0.5 kg block is released from rest a distance "h" above the ground. It slides on a frictionless surface, maximally compressing a spring with k=1000 N/m by 10 cm. Find "h".
Question
The 0.5 kg block is released from rest a distance "h" above the ground. It slides on a frictionless surface, maximally compressing a spring with k=1000 N/m by 10 cm. Find "h".
Solution
In each situation energy is conserved if heat effects and air resistance are negligible.
At the beginning, when the slingshot is "cocked"
Etotal = (0.5)mv2 + mgh + (0.5)kx2
Etotal = (0.5)m(0)2 + mg(0) + (0.5)(200.0)(0.500)2
Etotal = 25 J
The maximum velocity is obtained after the pebble is released but before it has achieved any altitude.
Etotal = (0.5)mv2 + mgh + (0.5)kx2
25 J = (0.5)(0.0100 kg)(v)2 + mg(0) + (0.5)k(0)2
v = 70.7 m/s
At its maximum height, the velocity of the pebble is zero.
Etotal = (0.5)mv2 + mgh + (0.5)kx2
25 J = (0.5)m(0)2 + (0.010 kg)(9.8 N/kg)h + (0.5)k(0)2
h = 255 m