To calculate the instantaneous velocity of the stone when released, we first need to calculate the potential energy stored in the rubber band when it is stretched.
The potential energy stored in a rubber band is given by the formula:
Potential Energy = (1/2) * spring constant * distance^2
Given that the distance the rubber band is stretched is 7cm and the average force is 70cm, we can plug in the values into the equation to find the potential energy:
Potential Energy = (1/2) * 70 * (0.07)^2
Potential Energy = 0.1715 J (approximately)
Next, we can use the principle of conservation of energy to find the kinetic energy of the stone when it is released. The potential energy is converted into kinetic energy when the stone is released.
Kinetic Energy = Potential Energy
Using the formula for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Given that the mass of the stone is 5g, we need to convert it to kilograms (as the SI unit for mass is kg):
Mass = 5g = 0.005kg
Plugging in the values, we have:
(1/2) * 0.005 * velocity^2 = 0.1715
Multiplying both sides by 2:
0.005 * velocity^2 = 0.343
Dividing both sides by 0.005:
velocity^2 = 0.343 / 0.005
velocity^2 = 68.6
Taking the square root of both sides:
velocity = √68.6
velocity ≈ 8.29 m/s
Therefore, the instantaneous velocity of the stone when released is approximately 8.29 m/s.
A stone of mass 5g is projected with a rubber catapult is stretched through a distance of 7cm by an average force of 7cm by an average force of 70cm , calculate the instaneous velocity of the stone when release
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1 answer