A STONE OF MASS 20g IS RELEASE FROM A CATAPULT WHOSE RUBBER IS STRETCHED THROUGH 5cm IF THE FORCE CONSTANT OF THE RUBBER IS 200N/m CALCULATE THE SPEED WITH WHICH THE STONE LEAVE THE CATAPULT
To calculate the speed with which the stone leaves the catapult, we can use the law of conservation of energy. The potential energy stored in the stretched rubber is converted into the kinetic energy of the stone.
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 ÷ 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 = √(25 m^2/s^2)
Velocity = 5 m/s
The speed with which the stone leaves the catapult is 5 m/s.
energy stored in spring = (1/2) k x^2
= (1/2)(200)(.05)^2
= kinetic energy of stone = (1/2)(.020) v^2