A stone of mass 5kg is projected with a rubber catapult. If the catapult is stretched through a distance of 7cm by the average of the force 70 N. Calculate the instateneous velocity when it is released
Work in = average force * distance = 70 N * 0.07 meter = 4.9 Joules
so
(1/2) m v^2 = 4.9 Joules
(1/2)(5) v^2 = 4.9
Its not correct pls
To calculate the instantaneous velocity of the stone when it is released, we need to use the concept of potential energy and kinetic energy.
Step 1: Calculate the potential energy stored in the stretched rubber band.
The potential energy (PE) stored in the rubber band is given by the formula:
PE = 0.5 * k * x^2
where k is the spring constant and x is the displacement (stretch) of the rubber band.
Step 2: Calculate the spring constant of the rubber band.
The spring constant (k) can be calculated using Hooke's Law:
F = k * x
where F is the force applied to stretch the rubber band and x is the displacement (stretch).
Step 3: Calculate the spring constant.
k = F / x
Given: force (F) = 70 N and displacement (x) = 7 cm = 0.07 m
k = 70 N / 0.07 m
k = 1000 N/m
Step 4: Calculate the potential energy stored in the rubber band.
PE = 0.5 * k * x^2
PE = 0.5 * 1000 N/m * (0.07 m)^2
PE = 0.245 J
Step 5: Calculate the kinetic energy of the stone.
The potential energy stored in the rubber band is converted into kinetic energy when the stone is released.
KE = PE
KE = 0.245 J
Step 6: Calculate the velocity of the stone.
The kinetic energy (KE) is related to the mass (m) and velocity (v) of the stone by the formula:
KE = 0.5 * m * v^2
We can rearrange this equation to solve for v:
v^2 = (2 * KE) / m
Substituting the values:
v^2 = (2 * 0.245 J) / 5 kg
v^2 = 0.098 J / kg
v^2 = 0.098 m^2/s^2
Taking the square root of both sides to find the velocity:
v = sqrt(0.098 m^2/s^2)
v ≈ 0.31 m/s
Therefore, the instantaneous velocity of the stone when it is released is approximately 0.31 m/s.
To calculate the instantaneous velocity of the stone when it is released, we need to use the principles of work and energy.
First, we need to calculate the potential energy stored in the rubber when it is stretched. The potential energy (Ep) is given by the formula:
Ep = (1/2) * k * x^2
Where:
Ep is the potential energy,
k is the spring constant of the rubber,
x is the displacement or stretch of the rubber.
In this case, the stretch of the catapult is given as 7 cm, which is equal to 0.07 meters. The force applied by the rubber is given as 70 N.
To calculate the spring constant (k), we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement.
F = k * x
Rearranging the equation, we can solve for the spring constant:
k = F / x
Substituting the values we have:
k = 70 N / 0.07 m
k = 1000 N/m
Now that we have the spring constant, we can calculate the potential energy:
Ep = (1/2) * (1000 N/m) * (0.07 m)^2
Ep = 2.45 Joules
The potential energy stored in the rubber when it is stretched is 2.45 Joules.
Next, we can equate this potential energy to the kinetic energy (Ek) of the stone when it is released.
Ek = (1/2) * m * v^2
Where:
Ek is the kinetic energy,
m is the mass of the stone,
v is the instantaneous velocity when released.
Rearranging the equation, we can solve for the instantaneous velocity:
v = sqrt(2 * Ep / m)
Substituting the values we have:
v = sqrt(2 * 2.45 J / 5 kg)
v = sqrt(0.98 J / kg)
v = 0.7 m/s
Therefore, the instantaneous velocity of the stone when it is released is 0.7 m/s.