A catapult used to hold a stone of mass 500grammes is extended by 2cm with an applied force F. if the stone leaves with a velocity 40ms-1, the value of F is.
To calculate the value of force (F), we can use the principle of conservation of mechanical energy. The potential energy stored in the extended catapult will be converted into the kinetic energy of the stone when it leaves the catapult.
The potential energy (PE) stored in the catapult can be calculated using the formula:
PE = 0.5 * k * x^2
Where:
k = spring constant of the catapult
x = extension of the catapult
Since the stone is extended by 2cm, we need to convert it into meters:
x = 2cm = 0.02m
Now, let's substitute the given values into the formula:
PE = 0.5 * k * (0.02)^2
PE = 0.5 * k * 0.0004
PE = 0.0002k
The potential energy stored in the catapult is equal to the kinetic energy of the stone when it leaves the catapult:
PE = KE
The kinetic energy (KE) of the stone can be calculated using the formula:
KE = 0.5 * m * v^2
Where:
m = mass of the stone
v = velocity of the stone
Substituting the given values into the formula:
KE = 0.5 * 0.5kg * (40m/s)^2
KE = 0.5 * 0.5kg * 1600m2/s2
KE = 400J
Now, equating the potential energy (PE) to the kinetic energy (KE):
0.0002k = 400
To find the value of k, we divide both sides of the equation by 0.0002:
k = 400 / 0.0002
k = 2,000,000 N/m
Finally, the value of force (F) can be calculated using Hooke's Law, which states that the force applied to extend or compress a spring is proportional to the extension or compression:
F = k * x
F = 2,000,000 N/m * 0.02 m
F = 40,000 N
Therefore, the value of force (F) required to extend the catapult by 2cm is 40,000 Newtons.