Answer:
14.1 m/s or 14 m/s for 2 sig figs. [5 cm is only 1 sig fig, but it was difficult writing 10 m/s after all that work]too
Explanation:
We can use the principle of conservation of mechanical energy to find the speed of the stone when launched by the catapult.
The mechanical energy of the system before launch should be equal to the mechanical energy after launch.
The mechanical energy consists of two components: potential energy and kinetic energy.
Potential Energy (PE):
The potential energy of the rubber band when stretched can be calculated using Hooke's Law for elastic potential energy:
PE = (1/2)kx^2
Where:
PE = Potential energy
k = Elastic constant (200 Newtons per meter)
x = Displacement (0.05 meters, as 5cm is equal to 0.05 meters)
PE = (1/2) * 200 N/m * (0.05 m)^2
PE = (1/2) * 200 N/m * 0.0025 m^2
PE = 0.25 Joules
Kinetic Energy (KE):
The kinetic energy of the stone after launch can be calculated using the formula for kinetic energy:
KE = (1/2)mv^2
Where:
KE = Kinetic energy
m = Mass of the stone (0.05 kg, as 50g is equal to 0.05 kg)
v = Velocity of the stone (the unknown)
According to the conservation of mechanical energy:
Initial Potential Energy (PE) = Final Kinetic Energy (KE)
0.25 Joules = (1/2) * 0.05 kg * v^2
Solving for v^2:
v^2 = (2 * 0.25 Joules) / 0.05 kg
v^2 = 10 Joules / 0.05 kg
v^2 = 200 m^2/s^2
v = √(200 m^2/s^2)
v ≈ 14.14 m/s
The catapult can give a speed of approximately 14.14 meters per second to the 50g stone when launched.
