A 1kg projectile is fired at 10m/s from a 10kg launcher. The momenta of the projectile and the launcher have the same magnitude, but opposite directions.
Show that the KE of the projectile is 10 times gerater that the KE of the recoiling launcher.
KE = 1/2mv^2?
do you add the 2 masses together?
I think I got it... you do two separate calculations, one w/ each mass
M1 V1 = M2 V2 = P (momentum of each)
KE1 = (1/2)M1V1^1 = (1/2)P^2/M1
KE2 = (1/2)M2V2^2 = (1/2)P^2/M2
KE1/KE2 = M2/M1
sd,, basically u wanna poo[p on dat lol
To find the kinetic energy (KE) of an object, you use the formula KE = 1/2mv^2, where m is the mass of the object and v is its velocity.
Let's consider the projectile and the launcher separately:
1. Projectile:
Given: Mass of the projectile (m1) = 1 kg, Velocity of the projectile (v1) = 10 m/s.
Using the formula for KE, we can calculate the KE of the projectile as follows:
KE1 = 1/2 * m1 * v1^2
= 1/2 * 1 kg * (10 m/s)^2
= 1/2 * 1 kg * 100 m^2/s^2
= 50 Joules
2. Launcher:
Given: Mass of the launcher (m2) = 10 kg, Velocity of the launcher (v2) = -10 m/s (opposite direction to the projectile).
Using the same formula for KE, we can calculate the KE of the launcher as follows:
KE2 = 1/2 * m2 * v2^2
= 1/2 * 10 kg * (-10 m/s)^2
= 1/2 * 10 kg * 100 m^2/s^2
= 500 Joules
Comparing the KE values, we find that KE1 (the KE of the projectile) is 10 times greater than KE2 (the KE of the launcher). The reason is that the kinetic energy is directly proportional to the square of the velocity.