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 70N, calculate the instantaneous velocity of the stone when released.
To find the instantaneous velocity of the stone when released, we can use the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy.
The work done by the catapult is equal to the force applied multiplied by the distance over which it is applied:
Work = force x distance
Work = 70N x 0.07m
Work = 4.9 J
This work done by the rubber catapult is equal to the change in kinetic energy of the stone. The initial kinetic energy of the stone is 0, so the final kinetic energy is equal to this work done by the catapult.
Final kinetic energy = 4.9 J
The kinetic energy of the stone is given by:
Kinetic energy = 1/2 * mass * velocity^2
Setting the final kinetic energy equal to this equation:
4.9 J = 1/2 * 0.005kg * velocity^2
Solving for velocity:
4.9 J = 0.0025kg * velocity^2
velocity^2 = 4.9 J / 0.0025 kg
velocity = sqrt(1960 m^2/s^2)
velocity = 44.27 m/s
Therefore, the instantaneous velocity of the stone when released is 44.27 m/s.