Yesterday our teacher gave this qn to solve which I doubt is solvable as time is not given in both situations.
The qn is:
A gun of mass 10kg fires a 100gm bullet with velocity 100m/s, calculate the recoiling velocity of gun and the force required to stop the gun within the distance 10cm
If the bullet strikes a wood block of 3.9kg placed on horizontal rough surface and the bullet is embedded inside the block find the distance travelled by block before coming to rest if coefficient of friction is 0.4.
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Smart way to ask others to do your homework with that title.
**1A. Conservation of linear momentum:**
Initial momentum of the gun and bullet system before firing is zero. When bullet of 0.1 kg is fired with a velocity of 100m/s, its momentum is now 10kgm/s.
However, momentum cannot appear out of thin air and thus the gun that fired the moment must have gained the same momentum in opposite direction. Thus, the gun has a recoil velocity of 1 m/s.
**1B. Equations of motion:**
An object with an initial velocity if 1 m/s needs to be decelerated such that it comes to stop within 0.1 m. Thus, initial velocity (u) = 1 m/s, final velocity (v) = 0, distance travelled = 0.1 m. Applying v^2 = u^2 + 2as, where a is acceleration and s is distance travelled, a = -5 m/s^2.
**1C. Newton’s 2nd law:**
F = ma. Thus, you will need to apply ____
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**2A. Conservation of linear momentum (again, yes.)**
Total momentum of bullet + block system = conserved. Thus, velocity of bullet + block system = (0.1*100)/(3.9+0.1) = 2.5 m/s.
**2B. Friction Force**
Friction Force = coeff. of friction x normal force = 0.4* (3.9+0.1)*9.81 = 15.696 N
This force provides retarding acceleration to the wood block, which can be evaluated by Newton’s 2nd law as 3.924 m/s^2
**2C. Back to equations of motion:**
Again, apply v^2 = u^2 + 2as, where v = 0, a = 3.924 m/s^2 to determine the distance travelled s.
You are missing the value for initial velocity of the block u, but surely by this point you are able to calculate it, right?
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**Moral of the story: The problem can be solved. You need to study a bit harder.**
*Disclaimer: no, I’m not your teacher, neither am I anybody you know irl.*