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
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.
To calculate the instantaneous velocity of the stone when released, we can use the concept of potential energy and kinetic energy.
1. Find the potential energy (PE) stored in the rubber band:
PE = force × distance
= 70 cm × 7 cm
= 490 cm^2
2. Convert the mass of the stone from grams to kilograms:
mass = 5 g = 0.005 kg
3. Calculate the potential energy in Joules (J):
PE (J) = PE (cm^2) × 0.1 J/cm^2 (conversion factor)
= 490 cm^2 × 0.1 J/cm^2
= 49 J
4. Apply the conservation of energy to find the kinetic energy (KE) of the stone when it is released:
KE (initial) = PE (final)
0 + 0.5 × mass × velocity^2 = 49 J
5. Rearrange the equation and solve for velocity (v):
0.5 × 0.005 kg × velocity^2 = 49 J
velocity^2 = 49 J / (0.5 × 0.005 kg)
velocity^2 = 49 J / 0.0025 kg
velocity^2 = 19,600 m^2/s^2
6. Take the square root of the equation to find the velocity:
velocity = sqrt(19,600 m^2/s^2)
velocity = 140 m/s
Therefore, the instantaneous velocity of the stone when released is 140 m/s.
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 stretched rubber band is converted into kinetic energy when released.
1. First, let's calculate the potential energy stored in the rubber band:
Potential energy (PE) = Force x Distance
PE = 70 N x 0.07 m (convert centimeters to meters)
PE = 4.9 Joules
2. Next, we can equate the potential energy to the kinetic energy of the stone:
KE = 1/2 mv^2 (where KE = kinetic energy, m = mass, and v = velocity)
Rearranging the equation, we get:
v^2 = (2 × KE) / m
Plugging in the values, we get:
v^2 = (2 × 4.9 J) / 0.005 kg (convert grams to kilograms)
v^2 = 1960 m^2/s^2
3. Now, we can solve for the instantaneous velocity, v:
v = √(1960 m^2/s^2)
v ≈ 44.27 m/s
Therefore, the instantaneous velocity of the stone when released from the rubber catapult is approximately 44.27 m/s.