A catapult used to hold a stone of mass 500g is extended by 20cm with an applied force F.If the stone leaves with a velocity of 40ms-1,the value of F is
400
X=vt
T=0.2/40=0.005s
A=v/t=40ms^-1/0.05s=8.0*10^3ms^-2
F=ma=0.5kg*8000ms^-2
=4.0*10^3N
Ok go ahead
To find the value of the applied force F, we can use the principles of Newton's laws of motion.
Step 1: Determine the change in potential energy.
When the catapult is extended by 20cm (or 0.2m), the stone gains potential energy. The change in potential energy can be calculated using the equation:
ΔPE = m * g * h
Where:
ΔPE is the change in potential energy
m is the mass of the stone (500g or 0.5kg)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height of the stone (0.2m)
ΔPE = (0.5kg) * (9.8 m/s^2) * (0.2m)
ΔPE = 0.98 Joules
Step 2: Determine the work done.
The work done on the stone by the applied force is equal to the change in potential energy. The work done can be calculated using the equation:
Work = force * distance
In this case, the distance is the extension of the catapult arm, which is 20cm or 0.2m. So we have:
Work = F * 0.2m
Since the work done is equal to the change in potential energy, we can equate the two expressions:
F * 0.2m = 0.98 Joules
Step 3: Solve for F.
To find the value of F, we rearrange the equation:
F = (0.98 Joules) / (0.2m)
F ≈ 4.9 Newtons
Therefore, the value of the applied force F is approximately 4.9 Newtons.