Why does a 10 gram bullet have more momentum traveling at 200m/s than at 20m/s?
To understand why a 10 gram bullet has more momentum when traveling at 200 m/s compared to when traveling at 20 m/s, we need to first understand the concept of momentum.
Momentum is a fundamental physical quantity that describes the motion of an object. It is defined as the product of an object's mass and velocity. Mathematically, momentum (p) is given by the equation:
p = m * v,
where p is momentum, m is mass, and v is velocity.
In this case, we have a 10 gram bullet, which means its mass (m) is 10 grams. However, it is important to note that when we calculate momentum, it is generally easier to work with mass in kilograms (kg) instead of grams (g). So, we need to convert the mass from grams to kilograms by dividing it by 1000:
m = 10 grams = 10 / 1000 kilograms = 0.01 kilograms.
Now let's compare the momentum of the bullet at two different velocities: 200 m/s and 20 m/s.
Case 1: Velocity = 200 m/s
Using the momentum equation, we can calculate the momentum of the bullet in this case:
p = m * v = 0.01 kg * 200 m/s = 2 kg*m/s.
Case 2: Velocity = 20 m/s
Similarly, we can calculate the momentum of the bullet at 20 m/s:
p = m * v = 0.01 kg * 20 m/s = 0.2 kg*m/s.
As you can see, the momentum of the bullet when it is traveling at 200 m/s is 2 kg*m/s, while the momentum when it is traveling at 20 m/s is 0.2 kg*m/s. Therefore, the bullet has more momentum when traveling at 200 m/s compared to 20 m/s.
The reason for this relationship can be explained by the fact that momentum depends on both mass and velocity. Since the velocity is squared in the momentum equation, a small change in velocity has a more significant effect on momentum compared to the same change in mass. In this case, the bullet's velocity is increasing by a factor of 10 (20 m/s to 200 m/s), resulting in a tenfold increase in momentum, while the mass remains the same.