Answer:
1. False
2. True
3. False
4. True
Explanation:
Conservation of Momentum
According to the law of conservation of linear momentum, the total momentum of the system formed by both pucks won't change regardless of their interaction if no external forces are acting on the system.
The momentum of an object of mass ma moving at speed va is
[tex]p_a=m_a.v_a[/tex]
The total momentum of both pucks at the initial condition is
[tex]p_1=m_a.v_a+m_b.v_b[/tex]
Both pucks are moving to the right and puck B has twice the mass of puck A (let's call it m), thus
[tex]m_a=m[/tex]
[tex]m_b=2m[/tex]
We are given
[tex]v_a=6\ m/s\\v_b=2\ m/s[/tex]
The total initial momentum is
[tex]p_1=6m+2(2m)=10m[/tex]
At the final condition, both pucks stick together, thus the total mass is 3m and the final speed is common, thus
[tex]p_2=3m.v'[/tex]
Equating the initial and final momentum
[tex]10m=3m.v'[/tex]
Solving for v'
[tex]v'=10/3\ m/s=3.33\ m/s[/tex]
1. Compute the initial kinetic energy:
[tex]\displaystyle K_1=\frac{1}{2}mv_a^2+\frac{1}{2}2mv_b^2[/tex]
[tex]\displaystyle K_1=\frac{1}{2}m\cdot 6^2+\frac{1}{2}2m\cdot 2^2[/tex]
[tex]K_1=18m+4m=22m[/tex]
The final kinetic energy is
[tex]\displaystyle K_2=\frac{1}{2}mv'^2+\frac{1}{2}2mv'^2[/tex]
[tex]\displaystyle K_2=\frac{1}{2}m\cdot 3.33^2+\frac{1}{2}2m\cdot 3.33^2[/tex]
[tex]K_2=16.63m[/tex]
As seen, part of the kinetic energy is lost in the collision, thus the statement is False
2. The initial speed of puck B was 2 m/s and the final speed was 3.33 m/s, thus it increased the speed: True
3. The initial speed of puck A was 6 m/s and the final speed was 3.33 m/s, thus it decreased the speed: False
4. The momentum is conserved since that was the initial assumption to make all the calculations. True
[tex]p_1=10m[/tex]
[tex]p_2=3m.v'=3m(10/3)=10m[/tex]
Proven
