A rifle with weight of 30N fires a 5.0g bullet with a speed of 300ms^-1.
a) Find the recoil speed of the rifle.
b) if a700N man holds the rifle firmly against his shoulder, find the recoil speed of man and rifle.
m = 30/9.81
a) (30/9.81)v = .005 * 300
b) (730/9.81)v = .005 * 300
To find the recoil speed of the rifle in both scenarios, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event. In this case, the event is the firing of a bullet.
The momentum of an object is calculated by multiplying its mass by its velocity.
a) Find the recoil speed of the rifle:
The momentum of the bullet before firing is given by the mass of the bullet (5.0g or 0.005kg) multiplied by its initial speed (300m/s):
Momentum of bullet before firing = 0.005kg * 300m/s = 1.5 kg·m/s
According to the conservation of momentum, the momentum of the rifle after firing should be equal in magnitude but opposite in direction to the momentum of the bullet.
The mass of the rifle is not given, but we know its weight, which is 30N. The weight of an object can be calculated by multiplying its mass by the acceleration due to gravity (9.8m/s²). Therefore, we can calculate the mass of the rifle using the following formula:
Weight = mass * acceleration due to gravity
30N = mass * 9.8m/s²
mass = 30N / 9.8m/s² ≈ 3.06kg
Now we can calculate the recoil speed of the rifle using the conservation of momentum:
Momentum of rifle after firing = -1.5 kg·m/s (opposite direction)
Recoil speed of rifle = Momentum of rifle after firing / mass of the rifle
Recoil speed of rifle = -1.5 kg·m/s / 3.06kg ≈ -0.49m/s (opposite direction)
Therefore, the recoil speed of the rifle is approximately 0.49m/s in the opposite direction of the bullet's initial velocity.
b) Find the recoil speed of the man and rifle:
In this case, the man is holding the rifle firmly against his shoulder, creating an external force of 700N opposing the recoil. We need to consider the total system comprising the man and the rifle.
Again, we use the conservation of momentum. Since the system consists of the man and the rifle, the total momentum before firing is zero because the man and the rifle are at rest.
The total momentum after firing should also be zero because there is no external force acting on the system.
Let's assume the recoil speed of the man is v_m and the recoil speed of the rifle is v_r.
According to the conservation of momentum:
(p_m + p_r) = 0
(mass_m * v_m) + (mass_r * v_r) = 0
Substituting the values, we have:
(700N / 9.8m/s² * v_m) + (3.06kg * v_r) = 0
Now we can solve this equation to find the recoil speed of the man and the rifle.
Therefore, the recoil speed of the man and the rifle can be determined by solving the equation resulting from the conservation of momentum.
0.5 m/s
1(30/9.81)v = .005 * 300
2.(730/9.81)0+0.005*300=(730/9.81+0.005)v
v=0.020m/s