A stone of mass 5g is projected with a rubber catapult. If the catapult is stretched through a distance of 7cm by an average force of 70 N . Calculate the instantaneous velocity of the stone when released
To calculate the instantaneous velocity of the stone when released, we can use the principle of conservation of energy. The potential energy stored in the catapult when it is stretched is equal to the kinetic energy of the stone when it is released.
The potential energy stored in the stretched catapult can be calculated using the formula:
Potential energy = (1/2) * k * x^2
where k is the spring constant and x is the distance the catapult is stretched.
The spring constant (k) can be calculated using Hooke's law:
k = F / x
where F is the average force applied to stretch the catapult.
Plugging in the values given in the problem:
F = 70 N
x = 7 cm = 0.07 m
k = 70 N / 0.07 m = 1000 N/m (spring constant)
Now we can calculate the potential energy:
Potential energy = (1/2) * 1000 N/m * (0.07 m)^2 = 2.45 J
Since the potential energy is converted to kinetic energy when the stone is released, we can equate the two:
Potential energy = Kinetic energy
2.45 J = (1/2) * m * v^2
where m is the mass of the stone and v is its instantaneous velocity.
Plugging in the values given in the problem:
m = 5 g = 0.005 kg
Rearranging the equation to solve for v:
v^2 = (2 * 2.45 J) / 0.005 kg
v^2 = 980 J/kg
v = sqrt(980 J/kg) ≈ 31.3 m/s
Therefore, the instantaneous velocity of the stone when released is approximately 31.3 m/s.