energy stored in spring = (1/2) k x^2
= (1/2)(200)(.05)^2
= kinetic energy of stone = (1/2)(.020) v^2
= (1/2)(200)(.05)^2
= kinetic energy of stone = (1/2)(.020) v^2
Step 1: Convert the mass of the stone from grams to kilograms.
The mass of the stone is 20g. To convert grams (g) to kilograms (kg), divide by 1000.
Mass of the stone = 20g รท 1000 = 0.02 kg
Step 2: Determine the potential energy stored in the stretched rubber.
The potential energy stored in a spring is given by the formula:
Potential Energy = 0.5 * k * x^2
where k is the force constant of the rubber and x is the displacement (stretch) of the rubber.
The force constant (k) of the rubber is given as 200 N/m, and the displacement (x) is 5 cm = 0.05 m.
Potential Energy = 0.5 * 200 N/m * (0.05 m)^2
= 0.5 * 200 N/m * 0.0025 m^2
= 0.25 Joules
Step 3: Convert the potential energy into the kinetic energy of the stone.
The kinetic energy (KE) of the stone is equal to the potential energy stored in the rubber.
Kinetic Energy = Potential Energy = 0.25 Joules
Step 4: Use the kinetic energy formula to calculate the speed of the stone.
The kinetic energy (KE) of an object is given by the formula:
Kinetic Energy = 0.5 * mass * velocity^2
We already know the mass of the stone (0.02 kg) and the kinetic energy (0.25 Joules). We can rearrange the formula to solve for velocity (speed).
Velocity^2 = (2 * Kinetic Energy) / mass
Velocity^2 = (2 * 0.25 Joules) / 0.02 kg
Velocity^2 = 2 * 12.5 m^2/s^2
Velocity^2 = 25 m^2/s^2
Velocity = โ(25 m^2/s^2)
Velocity = 5 m/s
The speed with which the stone leaves the catapult is 5 m/s.