[a bullet weighing 50gm hits a 10cm
wall with velocity 100ms-1 and comes out of the wall. If the frictional force on the bullet
while in the wall is assumed to be a constant 2000N then with what velocity does the bullet
come out of the wall?
v = V0 + a * t
F = m * a
s = .5 * a * t^2
where s = 0.01 m
V0 = 100 m / s
m = 0.5 kg
F = 2000 kg m/(s^2)
solving f=ma for a :
a = f/m = -2000/0.05 m/(s^2) = -40000 m/(s^2)
solving s = .5at^2 for t :
2s = at^2
2s/a = t^2
t = square root(2s/a)
t=square root (2 * 0.01m) / -40000 m/(s^2)
t = 0.0000005 s
so
v =100 m/s - 40000 m/(s^2) * .0000005 s * .0000005 s
v = 100 m/s - 0.00000010 m /s
v = 99.99999999 m/s
P.S. forgot to take square root in time
calculation. Should be t = .0007s
so
v = 100 - 40000 * .0007 * .0007
v = 100 - .02
v = 99.98 m /s
The given answer is root over 2000
To determine the velocity with which the bullet comes out of the wall, we need to apply the principle of conservation of mechanical energy.
The bullet's initial kinetic energy before hitting the wall can be calculated using the formula: KE = 0.5 * mass * velocity^2.
Given:
Mass of bullet (m) = 50 g = 0.05 kg
Initial velocity (u) = 100 m/s
The bullet's initial kinetic energy (KE₁) can be calculated as:
KE₁ = 0.5 * m * u^2
Next, we need to determine the work done by the frictional force on the bullet while it is in the wall. The work done (W) can be calculated as the force (f) multiplied by the displacement (s).
Given:
Force of friction (F) = 2000 N
Displacement of bullet in the wall (s) = 10 cm = 0.1 m
The work done (W) = F * s
Now, we can calculate the final velocity (v) of the bullet as it comes out of the wall.
According to the principle of conservation of mechanical energy:
Initial kinetic energy (KE₁) - Work done (W) = Final kinetic energy (KE₂)
KE₂ = KE₁ - W
Finally, we can calculate the final velocity (v) using the formula:
v = sqrt((2 * KE₂) / m)
Let's substitute the given values and calculate the final velocity:
KE₁ = 0.5 * 0.05 * 100^2
W = 2000 * 0.1
KE₂ = KE₁ - W
v = sqrt((2 * KE₂) / m)
By solving these equations, we can find the velocity with which the bullet comes out of the wall.