A rifle with a weight of 30 N fires a 3.0 g bullet with a speed of 250 m/s.
(a) Find the recoil speed of the rifle.
(b) If a 675 N man holds the rifle firmly against his shoulder, find the recoil speed of the man and rifle.
I got .245 m/s for the first one but I keep getting the second wrong, how do I do it?
To find the recoil speed of the rifle, we can use the principle of conservation of momentum. According to this principle, the momentum before the bullet is fired is equal to the momentum after the bullet is fired.
(a) Recoil speed of the rifle:
1. Start by calculating the momentum of the bullet. Momentum (p) is calculated by multiplying the mass (m) of an object by its velocity (v): p = m * v.
Given:
mass of the bullet (m) = 3.0 g = 0.003 kg (convert grams to kilograms)
velocity of the bullet (v) = 250 m/s
Therefore, the momentum of the bullet is:
p_bullet = 0.003 kg * 250 m/s = 0.75 kg·m/s.
2. Since there is no external force acting on the rifle-bullet system, the total momentum before firing must be equal to the total momentum after firing.
The momentum of the rifle before firing is initially zero since it is at rest.
Therefore, the total momentum before firing is: p_total_before = 0 + 0 = 0 kg·m/s.
3. Since the rifle and bullet are initially at rest, the total momentum after firing is only due to the bullet.
The momentum of the bullet after firing is the same as calculated in step 1: p_bullet = 0.75 kg·m/s.
Therefore, the total momentum after firing is: p_total_after = p_bullet = 0.75 kg·m/s.
4. Using the principle of conservation of momentum, we can equate the total momentum before firing (step 2) to the total momentum after firing (step 3):
p_total_before = p_total_after.
0 = 0.75 kg·m/s.
5. To find the recoil speed of the rifle (v_rifle), we can rearrange the equation and solve for v_rifle:
v_rifle = - p_bullet / (mass of the rifle).
Given:
mass of the rifle = weight / acceleration due to gravity.
Since the weight of the rifle is given as 30 N, we need to convert it to kilograms:
mass of the rifle = 30 N / 9.8 m/s² = 3.06 kg (approximately).
Substitute the known values into the equation:
v_rifle = - 0.75 kg·m/s / 3.06 kg ≈ -0.245 m/s.
Therefore, the recoil speed of the rifle is approximately -0.245 m/s (the negative sign indicates that the rifle moves in the opposite direction of the bullet).
(b) Recoil speed of the man and rifle:
1. The man is exerting a force on the rifle, which will affect the recoil speed. To find the recoil speed of the man and rifle combined, we can incorporate the force exerted by the man into the momentum equation.
The momentum equation in this case becomes:
p_total_before = p_total_after + p_man,
where p_total_before is zero since the system is initially at rest, p_total_after is the momentum of the bullet as calculated in step 3, and p_man is the momentum of the man.
2. To calculate the momentum of the man (p_man), we can use the same formula: p = m * v.
Given:
mass of the man = 675 N (weight of the man) / 9.8 m/s² (acceleration due to gravity).
Convert the weight of the man to kilograms:
mass of the man = 675 N / 9.8 m/s² ≈ 68.9 kg.
3. Since the man is initially at rest, the momentum before firing is zero: p_man_before = 0 kg·m/s.
4. Substitute the known values into the momentum equation in step 1 and solve for p_man_after:
0 = 0.75 kg·m/s + p_man_after.
p_man_after = -0.75 kg·m/s.
5. The recoil speed of the man and rifle combined (v_man+rifle) can be calculated using the formula: v_man+rifle = p_man_after / (mass of the man + mass of the rifle).
Substitute the known values into the equation:
v_man+rifle = -0.75 kg·m/s / (68.9 kg + 3.06 kg) ≈ -0.0107 m/s.
Therefore, the recoil speed of the man and rifle combined is approximately -0.0107 m/s.