A bullet with a mass of 10. g is fired from a rifle with a barrel that is 85 cm long.
a. Assuming that the force exerted by the expanding gas to be a constant 5500 N, what speed would the bullet reach?
F = ma
v^2 = 2as
Wouldn't that be 967 m/s
To find the speed of the bullet, we can use the principle of conservation of momentum. The momentum before firing is equal to the momentum after firing.
1. Calculate the initial momentum:
- The initial momentum (p_initial) is given by the formula p = m * v, where m is the mass of the bullet and v is its velocity.
- Convert the mass of the bullet from grams to kilograms: 10 g = 0.01 kg.
- The initial velocity (v_initial) is 0 since the bullet is at rest initially.
- Therefore, p_initial = m * v_initial = 0.
2. Calculate the final momentum:
- The final momentum (p_final) is given by p = m * v, where m is the mass of the bullet and v is its final velocity.
- The force exerted by the expanding gas (F) is constant at 5500 N.
- The distance over which the force is applied (d) is the length of the barrel, 85 cm.
- The work done by the force is given by the formula W = F * d.
- Since work done is equal to the change in kinetic energy, we can equate W to the change in kinetic energy (ΔKE).
- ΔKE = 0.5 * m * v^2, where m is the mass of the bullet and v is its final velocity.
- Therefore, W = ΔKE = 0.5 * m * v^2.
3. Substitute the values and solve for the velocity:
- Using the equation W = F * d and W = ΔKE, we can equate the two expressions and solve for v.
- 0.5 * m * v^2 = F * d.
- 0.5 * 0.01 kg * v^2 = 5500 N * 0.85 m.
- Simplifying, we get v^2 = (5500 N * 0.85 m) / (0.5 * 0.01 kg).
- v^2 = 935000 m^2/s^2.
- Taking the square root of both sides, we get v ≈ 966.1 m/s.
Therefore, the speed of the bullet would be approximately 966.1 m/s.
To find the speed of the bullet, we can use the principle of conservation of energy. Let's break down the steps to get the answer:
Step 1: Calculate the work done on the bullet.
The work done on an object is given by the equation:
Work = Force x Distance
In this case, the force acting on the bullet is the force exerted by the expanding gas (5500 N), and the distance is the length of the barrel (85 cm = 0.85 m). Therefore, the work done on the bullet can be calculated as:
Work = 5500 N x 0.85 m
Step 2: Calculate the kinetic energy of the bullet.
The work done on the bullet is converted into the bullet's kinetic energy. So we can equate the work done to the kinetic energy equation:
Work = Kinetic Energy = (1/2) x mass x velocity^2
In this case, the mass of the bullet is given as 10 g, but we need to convert it to kilograms by dividing by 1000:
mass = 10 g / 1000 = 0.01 kg
So the equation becomes:
5500 N x 0.85 m = (1/2) x 0.01 kg x velocity^2
Step 3: Solve for the velocity.
Rearrange the equation to solve for the velocity:
velocity^2 = (5500 N x 0.85 m) / (0.01 kg x (1/2))
velocity^2 = 5500 N x 0.85 m / 0.005 kg
velocity^2 = 935,000 m^2/s^2
velocity = sqrt(935,000) m/s
Now, you can calculate the square root of 935,000 to find the velocity of the bullet.
Therefore, the speed the bullet would reach is approximately 966.09 m/s.