Two 3.0g bullets are fired with speeds of 40.0 m/s and 80.0 m/s respectively. What are their kinetic energies? Which bullet has more kinetic energy? What is the ratio of their kinetic energies?
I got 60 for the first bullet and 120 for the second. I am not sure I used the formula correctly and I do not know how to obtain the "ratio" for kinetic energies. I would appreciate any help.
no clue
you are correct. The ratio would be 2:1 (13 years later)
To calculate the kinetic energy of an object, you can use the formula:
Kinetic energy (KE) = (1/2) * mass * velocity^2
Let's apply this formula to calculate the kinetic energies of the two bullets:
For the first bullet:
Mass (m1) = 3.0g = 0.003 kg
Velocity (v1) = 40.0 m/s
KE₁ = (1/2) * m₁ * v₁^2
= (1/2) * 0.003 * 40.0^2
= 24 J
For the second bullet:
Mass (m2) = 3.0g = 0.003 kg
Velocity (v2) = 80.0 m/s
KE₂ = (1/2) * m₂ * v₂^2
= (1/2) * 0.003 * 80.0^2
= 96 J
Therefore, the first bullet has a kinetic energy of 24 J, while the second bullet has a kinetic energy of 96 J.
To determine which bullet has more kinetic energy, we can simply compare their values. In this case, the second bullet (with 96 J of kinetic energy) has more kinetic energy than the first bullet (with 24 J of kinetic energy).
The ratio of their kinetic energies can be calculated by dividing the kinetic energy of the second bullet (KE₂) by the kinetic energy of the first bullet (KE₁):
Ratio = KE₂ / KE₁
= 96 J / 24 J
= 4
Therefore, the ratio of their kinetic energies is 4:1, meaning the second bullet has four times the kinetic energy of the first bullet.
To calculate the kinetic energy of an object, you need to use the formula: KE = 1/2 * m * v^2, where KE represents the kinetic energy, m is the mass of the object, and v is its velocity.
For the first bullet:
Mass (m) = 3.0 g = 0.003 kg
Velocity (v) = 40.0 m/s
To calculate the kinetic energy:
KE1 = 1/2 * 0.003 kg * (40.0 m/s)^2
KE1 = 1/2 * 0.003 kg * 1600 m^2/s^2 = 2.4 J (joules)
For the second bullet:
Mass (m) = 3.0 g = 0.003 kg
Velocity (v) = 80.0 m/s
To calculate the kinetic energy:
KE2 = 1/2 * 0.003 kg * (80.0 m/s)^2
KE2 = 1/2 * 0.003 kg * 6400 m^2/s^2 = 9.6 J (joules)
Therefore, the first bullet has a kinetic energy of 2.4 J, while the second bullet has a kinetic energy of 9.6 J.
To find the ratio of their kinetic energies, divide the kinetic energy of the second bullet (KE2) by the kinetic energy of the first bullet (KE1):
Ratio = KE2 / KE1
Ratio = 9.6 J / 2.4 J = 4
So, the ratio of their kinetic energies is 4:1, indicating that the second bullet has four times more kinetic energy than the first bullet.