Answer:
The common speed is 1.95 m/s
Explanation:
Law Of Conservation Of Linear Momentum
It states that the total momentum of a system of bodies is conserved unless an external force is applied to it. The formula for the momentum of a body with mass m and velocity v is
P=mv.
If we have a system of bodies, then the total momentum is the sum of all of them:
[tex]P=m_1v_1+m_2v_2+...+m_nv_n[/tex]
If a collision occurs, the velocities change to v' and the final momentum is:
[tex]P'=m_1v'_1+m_2v'_2+...+m_nv'_n[/tex]
In a system of two masses, the law of conservation of linear momentum
is written as:
[tex]m_1v_1+m_2v_2=m_1v'_1+m_2v'_2[/tex]
If both masses stick together after the collision at a common speed v', then:
[tex]m_1v_1+m_2v_2=(m_1+m_2)v'[/tex]
The common velocity after this situation is:
[tex]\displaystyle v'=\frac{m_1v_1+m_2v_2}{m_1+m_2}[/tex]
The truck of m1=1200 N (weight) travels at v1=2 m/s and hits a stationary mass (v2=0) of m2=30 N (weight). After the bodies collide, they keep moving together. Before we can calculate the common speed, we need to calculate the masses of the bodies, since they are given as weights.
[tex]m_1=\frac{P_1}{g}=\frac{1200}{9.8}=122.45 Kg[/tex]
[tex]m_2=\frac{P_2}{g}=\frac{30}{9.8}=3.06 Kg[/tex]
Now calculate the common speed:
[tex]\displaystyle v'=\frac{122.45 * 2+3.06 * 0}{122.45+3.06}[/tex]
[tex]\displaystyle v'=\frac{244.9}{125.51}=1.95\ m/s[/tex]
The common speed is 1.95 m/s
