A catapult used to hold a stone of mass 500g is extended by 20cm with applied force .f if the stone leaves with a velocity of 40m/s,what is the value of f?
Help plz
(1/2) m v^2 = (1/2) k x^2
.5 (1600) = .5 k (.04)
k = 40,000 Newtons/meter
F = k x = 40,000 (.2) = 8000 N
0.5 x 0.5(1600) = 0.5 x k x 0.04
K=20,000
F=4,000
To find the value of force (f), we can use Newton's second law of motion:
F = ma
Where:
F = force (in Newtons)
m = mass (in kilograms)
a = acceleration (in meters per second squared)
First, let's convert the mass of the stone to kilograms:
Given mass = 500g = 0.5kg
Next, we need to find the acceleration. We can do this using the equation for acceleration:
a = (v - u) / t
Where:
v = final velocity (in meters per second)
u = initial velocity (which in this case is 0 since the stone starts from rest)
t = time taken (which we need to calculate)
We can calculate the time taken for the stone to leave the catapult using the formula:
v = u + at
40 m/s = 0 + a * t
Since the initial velocity (u) is 0, the equation simplifies to:
40 m/s = a * t
Now, let's find the time taken (t):
t = 40 m/s / a
To determine the value of acceleration (a), we can use the equation:
a = (v^2 - u^2) / 2d
Where:
d = distance (which is the extension of the catapult)
v = final velocity
u = initial velocity
In this case, the stone started at rest (u = 0), so we have:
a = v^2 / 2d
We know the final velocity (v = 40 m/s) and the extension (d = 20 cm = 0.2 m), so we can substitute these values into the equation to find the acceleration (a).
a = (40 m/s)^2 / (2 * 0.2 m)
Now that we have the acceleration (a), we can substitute it into the equation to find the time taken (t).
t = 40 m/s / a
Finally, we can substitute the time taken and the mass of the stone into the formula for force (F = ma) to find the value of force (f).
F = m * a
f = 0.5 kg * a
Now you can plug in the calculated value of acceleration (a) and solve for f to obtain the answer.
According to Newton's second law
F = ma
a = v^2/2d
a = 1,600/0.4 = 4,000
:. F = 0.5 × 4000 = 2,000N