To determine the instantaneous velocity of the stone when released from the catapult, we can use the principle of conservation of energy.
The potential energy stored in the stretched catapult is converted into the kinetic energy of the stone when it is released.
The potential energy (PE) stored in the stretched catapult can be calculated using the formula:
PE = 0.5 * k * x²
Where: k is the spring constant of the catapult x is the distance the catapult is stretched (7 cm = 0.07 m)
The spring constant (k) can be calculated using Hooke's Law:
k = F / x
Where: F is the average force applied to the catapult (7 N) x is the distance the catapult is stretched (0.07 m)
Substituting the values, we get:
k = 7 N / 0.07 m k = 100 N/m
Now, we can calculate the potential energy (PE) stored in the catapult:
PE = 0.5 * 100 N/m * (0.07 m)² PE = 0.245 J
According to the principle of conservation of energy, the potential energy stored in the catapult is equal to the kinetic energy of the stone when it is released:
PE = KE
KE = 0.245 J
The kinetic energy (KE) can be calculated using the formula:
KE = 0.5 * m * v²
Where: m is the mass of the stone (5 g = 0.005 kg) v is the instantaneous velocity of the stone when released
Substituting the values, we have:
0.245 J = 0.5 * 0.005 kg * v² 0.245 J = 0.0025 kg * v²
Dividing both sides by 0.0025 kg, we get:
v² = 0.245 J / 0.0025 kg v² = 98 m²/s²
Taking the square root of both sides, we find:
v = √(98 m²/s²) v ≈ 9.9 m/s
Therefore, the instantaneous velocity of the stone when released from the catapult is approximately 9.9 m/s.