Two bullets have masses of 2.4 g and 5.2 g, respectively. Each is fired with a speed of 37.0 m/s.
a) What is the kinetic energy of the first
bullet?
b) What is the kinetic energy of the second bullet?
I initially used KE=1/2MV^2 and got 1642.8 J, but got it wrong. What is my mistake?
Mass is measurd in kg Not grams. S0 you
must convert to kg:
divide grams by 1000.
I see! Thank you!
Another quick question, what is the ratio
K2/K1 of their kinetic energies. Is, it just dividing the second bullet's KE to the first?
The ratio of K2 to K1 = K2/K1.
The ratio of K1 to K2 = K1/K2.
Your mistake lies in using the wrong formula for calculating kinetic energy. The correct formula for kinetic energy is KE = 1/2 mv^2, where m is the mass of the object and v is its velocity. In your calculation, you used the formula KE = 1/2 MV^2, but with the correct values plugged in, you should get the correct answers.
Let's calculate the kinetic energy of each bullet using the correct formula:
a) For the first bullet:
Mass (m1) = 2.4 g = 0.0024 kg
Velocity (v1) = 37.0 m/s
Using the formula KE = 1/2 mv^2:
KE1 = 1/2 * 0.0024 kg * (37.0 m/s)^2
= 1/2 * 0.0024 kg * 1369 m^2/s^2
= 0.0012 kg * 1369 m^2/s^2
≈ 1.64688 J
≈ 1.65 J (rounded to two decimal places)
So, the kinetic energy of the first bullet is approximately 1.65 Joules.
b) For the second bullet:
Mass (m2) = 5.2 g =0.0052 kg
Velocity (v2) = 37.0 m/s
Using the formula KE = 1/2 mv^2:
KE2 = 1/2 * 0.0052 kg * (37.0 m/s)^2
= 1/2 * 0.0052 kg * 1369 m^2/s^2
= 0.0026 kg * 1369 m^2/s^2
≈ 3.5188 J
≈ 3.52 J (rounded to two decimal places)
So, the kinetic energy of the second bullet is approximately 3.52 Joules.
Therefore, your original answer of 1642.8 J was incorrect because you used the wrong formula. By using the correct formula KE = 1/2 mv^2, you can get the accurate values of kinetic energy for each bullet.