A gun is fired, and a 50gram bullet is accelerated to a muzzle speed of 100m/s. If the length of the gun barrel is 0.90m, what is the magnitude of the accelerating force? Assume the acceleration is constant.
Help me please???
acceleration = change in velocity/change in time
magnitude of change in velocity = 100 m/s
(all in one direction)
time = distance/average speed = 0.9/50
= 1.8/100 = .018
a = 100/.018
F = m a = .050*100/.018 = 278 m/s^2
which is about 28 times gravity
v² = 2ax
100² = 2*0.9a
a =100² /1.8 = 5555.56
Force = ma = 0.05 x 5555.56 = 278 N
Thanks guys! I appreciate your help!
You are welcome. Now you have two ways to do it, both valid.
To find the magnitude of the accelerating force in this scenario, we can use the equation for linear motion:
F = m * a
F is the force,
m is the mass of the object, and
a is the acceleration.
In this case, the mass of the bullet is given as 50 grams, which can be converted to kilograms:
m = 50 grams = 0.05 kg
The acceleration is not directly given, but we can calculate it using the equation of linear motion:
v^2 = u^2 + 2aS
v is the final velocity,
u is the initial velocity,
a is the acceleration, and
S is the displacement.
In this case, the initial velocity is 0 m/s (as the bullet starts from rest), the final velocity is 100 m/s, and the displacement is given as the length of the gun barrel, which is 0.90 m. Rearranging the equation, we get:
a = (v^2 - u^2) / (2S)
Substituting the values, we get:
a = (100^2 - 0^2) / (2 * 0.90)
Now we can substitute the calculated mass and acceleration in the previous equation to find the force:
F = m * a
F = 0.05 kg * [(100^2 - 0^2) / (2 * 0.90)]
Simplifying the equation, we get:
F = 0.05 kg * [(10000) / (1.8)]
Finally, calculating the value, we find that the magnitude of the accelerating force is approximately 2777.78 Newtons (N).
F ≈ 2777.78 N