A rifle fires a(n) 5 g bullet with a muzzle
velocity of 360 m/s into a block of wood. The bullet comes to rest after it has made a(n)19 cm deep hole in the wood.A rifle fires a(n) 5 g bullet with a muzzle
velocity of 360 m/s into a block of wood. The bullet comes to rest after it has made a(n)19 cm deep hole in the wood.
you can use the idea that the kinetic energy equals the amount of work of friction (Force of friction*d).
Use F(force of friction)= (m(v^2))/2d
...so F=(.005*(360^2))/2*.19= 1705.263 N
you use .005 because the mass was given in grams and the unit of N is kg*m/s so you have to convert 5g to .005kg and 19cm to .19m
To find the average force exerted by the bullet on the block of wood, we can use the principle of work and energy.
Step 1: Find the initial kinetic energy of the bullet.
The initial kinetic energy (KE) is given by the formula:
KE = (1/2) * m * v^2
where m is the mass of the bullet and v is the muzzle velocity of the bullet.
Given:
Mass of the bullet, m = 5 g = 0.005 kg
Muzzle velocity, v = 360 m/s
KE = (1/2) * 0.005 kg * (360 m/s)^2
KE = 0.5 * 0.005 kg * 129600 m^2/s^2
KE = 324 J
Step 2: Find the work done by the bullet to stop.
The work done (W) by the bullet is equal to the change in kinetic energy.
W = ΔKE
Since the bullet comes to rest, the change in kinetic energy is equal to the initial kinetic energy, but with a negative sign.
W = -324 J
Step 3: Find the average force exerted by the bullet on the wood.
The average force (F) exerted by the bullet is given by the equation:
F = W / d
where d is the distance over which the force is applied.
Given:
Depth of the hole, d = 19 cm = 0.19 m
F = (-324 J) / (0.19 m)
F ≈ -1705.26 N
Therefore, the average force exerted by the bullet on the block of wood is approximately -1705.26 N. The negative sign indicates that the force is exerted in the opposite direction of motion.
To find the force exerted by the bullet on the wood, we can calculate the deceleration experienced by the bullet using the equation of motion:
v^2 = u^2 + 2as
where:
v = final velocity (0 m/s, as the bullet comes to rest)
u = initial velocity (360 m/s)
a = acceleration (the deceleration of the bullet)
s = displacement (19 cm = 0.19 m, as the bullet penetrates 19 cm deep into the wood)
Rearranging the equation:
a = (v^2 - u^2) / (2s)
Substituting the given values:
a = (0 - 360^2) / (2 * 0.19)
a = -129474 / 0.38
a ≈ -340979 m/s^2
Since force (F) is related to mass (m) and acceleration (a) through the equation:
F = m * a
Substituting the mass of the bullet (5 g = 0.005 kg) and the obtained acceleration:
F = 0.005 kg * (-340979 m/s^2)
F ≈ -1705 N
Therefore, the force exerted by the bullet on the wood is approximately 1705 Newtons. The negative sign indicates that the force is in the opposite direction of the bullet's initial motion.