What is kinetic energy after collision of mass 4kg moving 6m/s in +y direction collids and stick to another object with mass 2kg moving at 4m/s in +x direction.
First apply conservation of momentum to get the final velocity V of the stuck-together masses. It will have both x and y components
The x-component of the final velocity is Vx = 2*4/(M1+M2) = 8/6 = 1.333 m/s
The y-component of the final velocity is
Vy = 4*6/(M1+M2) = 42/6 = 4.000 m/s
The final KE is (1/2)(M1+M2)V^2
= (1/2)(M1+M2)(Vx^2 + Vy^2)
= 53.33 J
(Note that the initial KE was 72 + 16 = 88 J)
To determine the kinetic energy after the collision, we need to consider the conservation of linear momentum and the law of conservation of energy.
First, let's calculate the initial total momentum before the collision:
Initial momentum in the x-direction:
Mass (m1) × Velocity (v1) = 4 kg × 6 m/s = 24 kg·m/s
Initial momentum in the y-direction:
Mass (m2) × Velocity (v2) = 2 kg × 4 m/s = 8 kg·m/s
Since there are no external forces acting on the system, the total momentum before the collision is conserved. Therefore, the total momentum after the collision will be the same as the initial total momentum.
Total momentum after the collision = 24 kg·m/s + 8 kg·m/s = 32 kg·m/s
Now, let's calculate the final velocity of the combined objects after the collision. Since they stick together, we can consider them as a single object with a total mass (m1 + m2) and a final velocity (vf).
Using the conservation of momentum:
Total momentum after the collision = Total mass × Final velocity
32 kg·m/s = (4 kg + 2 kg) × vf
32 kg·m/s = 6 kg × vf
vf = 32 kg·m/s ÷ 6 kg = 5.33 m/s
Now that we have the final velocity, we can calculate the kinetic energy after the collision.
Kinetic energy (KE) = 1/2 × Total mass × Final velocity^2
KE = 1/2 × (4 kg + 2 kg) × (5.33 m/s)^2
KE = 1/2 × 6 kg × 28.44 m^2/s^2
KE = 170.64 J
Therefore, the kinetic energy after the collision is 170.64 Joules.