Answer:
ΔK= -1741. 09 J
Explanation:
Theory of collisions
Linear momentum is a vector magnitude (same direction and direction as 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 : Initial linear momentum quantity
Nomenclature and data
m₁: block 1 mass = 3.90 kg
V₀₁: initial block 1 speed, =31.0m/s
Vf₁: final block 1 speed
m₂: block 2 mass = 51.0 kg
V₀₂: initial block 2 speed= 0
Vf₂: final block 2 speed
Problem development
For this problem the collision is plastic ,then, the blocks stick together after the collision and Vf₁=Vf₂=Vf
We assume that the Block 1 moves to the right before the collision (+) and The joined blocks move to the right after the collision(+).
We apply formula (1)
P₀=Pf
m₁*V₀₁+m₂*V₀₂=m₁*Vf₁+m₂*Vf₂
m₁*V₀₁+m₂*V₀₂=(m₁+m₂) Vf
3.9*31+51*0=(3.9+51) Vf
120.9+0 = 54.9*Vf
Vf = 120.9/54.9
Vf = 2.2 m/s
ΔK in the two-block system's kinetic energy due to the collision
ΔK=Kfinal−Kinitial
ΔK: Change in kinetic energy (J)
Kfinal: final kinetic energy (J)
Kinitial : initial kinetic energy (J)
Kinitial=(1/2 )m₁*V₀₁²+(1/2 )m₂*V₀₂²= (1/2 )(3.9)*(31)²+(1/2 )(51)*0=1873.95 J
Kfinal = (1/2 )(m₁+m₂)*Vf²= (1/2 )(3.9+51)* (2.2)² = 132.85 J
ΔK= 132.85 J−1873.95 J
ΔK= -1741. 09 J
