Answer:
Kf = 41 J
Explanation:
Theory of collisions
Linear momentum is a vector magnitude (same direction of the velocity) and its magnitude is calculated like this:
p=m*v
Where :
p : Linear momentum
m: mass
v:velocity
There are 3 cases of collisions : elastic, inelastic and plastic.
For the three cases the total linear momentum quantity is conserved:
P₀ = Pf Formula (1)
P₀ :Initial linear momentum quantity
Pf : Final linear momentum quantity
Data
m₁= 8.0-kg : mass of object₁
m₂= 2.0-kg : mass of object₂
v₀₁ = 4.0 m/s , to the right : Initial velocity of m₁
v₀₂= 3.0 m/s, to the left : Initial velocity of m₂
vf₁ = 2.0 m/s , to the right :Final velocity of m₁
Problem development
We assume that the 2kg object move to the right at the end of the collision, so, the sign of the final speeds (vf₂), we assume vf₂ positive:
We appy the formula (1):
P₀ = Pf
m₁*v₀₁ + m₂*v₀₂ = m₁*vf₁ + m₂*vf₂
(8)*(4) + (2)*(-3) = (8)*(2) +(2)*vf₂
32-6 = 16 + (2)*vf₂
32-6-16 = (2)*vf₂
10 = (2)*vf₂
vf₂ = 10 / (2)
vf₂ = 5 m/s, to the right
Kinetic energy
Kinetic energy is that which is due to the movement of bodies and is calculted like this:
K = (1/2)mv²
Where:
K : Kinetic energy (J)
m: mass (kg)
v : speed (m/s)
Total kinetic energy of the two-mass system after the collision (Kf)
Kf = Kf₁ +Kf₂
Kf₁ = (1/2)m₁vf₁² = (1/2)(8)(2)² = 16 J
Kf₂ = (1/2)m₂vf₂² = (1/2)(2)(5)² =25 J
Kf = 16 J+ 25 J
Kf = 41 J
The total kinetic energy of the two-mass system after the collision is mathematically given as
Kf= 41 J
Question Parameter(s):
An 8.0-kg object moving 4.0 m/s in the positive x-direction
with a 2.0-kg object moving 3.0 m/s in the opposite direction.
The final velocity of the 8.0-kg object is 2.0 m/s
Generally, the equation for the conservation momentum is mathematically given as
m1*v₀₁ + m2*v2 = m1*vf1 + m2*vf2
Therefore
(8)*(4) + (2)*(-3) = (8)*(2) +(2)*vf2
32-6 = 16 + (2)*vf2
32-6-16 = (2)*vf2
10 = 2*vf₂
vf2 = 10 / (2)
vf2 = 5 m/s,
In conclusion, Kinetic energy
Kf = Kf₁ +Kf₂
Kf1 = (1/2)m₁vf₁² = (1/2)(8)(2)²
Kf1= 16 J
Kf2 = (1/2)m2vf2^2
Kf2= (1/2)(2)(5)^2
Kf2=25 J
Therefore
Kf = 16 J+ 25 J Kf
Kf= 41 J
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