a bullet of mass 20g travelling at 16m/s penetrates a brock of wood and it comes to rest in 0.5seconds.find(a)the acceralation (b)the average redating force(c)the depth of the penetration
Assuming that the wood block is fixed and stationary.
(a)
acceleration, a
= (final vel. - initial vel) / time
= (v-u)/t
= (0-16 m/s) / 0.5
= -32 m/s²
(b)
average force
= mass * acceleration
= 0.020 kg * 32 m/s²
= 0.64 newton
(c)
Distance, S
= ut+(1/2)at²
= 16*0.5+(1/2)*(-32)*(0.5^2)
= 8+(-4)
= 4 m
To find the answer to these questions, we can use the principles of Newton's laws of motion and equations of motion.
(a) To find the acceleration (a), we can use the equation:
v = u + at
Where:
v = final velocity (0 m/s in this case, as the bullet comes to rest)
u = initial velocity (16 m/s)
a = acceleration
t = time (0.5 seconds)
Rearranging the equation to isolate a, we have:
a = (v - u) / t
Substituting the given values, we get:
a = (0 - 16) / 0.5
a = -32 m/s^2
Therefore, the acceleration of the bullet is -32 m/s^2 (negative sign indicates deceleration).
(b) To find the average retarding force (F), we can use Newton's second law of motion:
F = m * a
Where:
m = mass of the bullet (20 g = 0.02 kg)
a = acceleration (-32 m/s^2)
Substituting the given values, we get:
F = 0.02 kg * (-32 m/s^2)
F = -0.64 N
Therefore, the average retarding force on the bullet is -0.64 N (negative sign indicates opposition to the bullet's motion).
(c) To find the depth of penetration, we need to use the concept of work done. The work done can be equated to the change in kinetic energy (KE) of the bullet.
The change in KE is given by the equation:
ΔKE = KE_final - KE_initial
Where:
KE = (1/2) * m * (v^2)
Initial KE is (1/2) * 0.02 kg * (16 m/s)^2 = 2.56 J
Final KE is 0 J (as the bullet comes to rest)
Therefore, ΔKE = 0 - 2.56 J = -2.56 J
The work done (W) is also given by:
W = F * d
Where:
F = average retarding force (-0.64 N)
d = depth of penetration (what we want to find)
Substituting the values, we get:
-2.56 J = -0.64 N * d
Solving for d, we have:
d = (-2.56 J) / (-0.64 N)
d = 4 meters
Therefore, the depth of penetration is 4 meters.