Answer :
Explanation:
The given data is as follows.
Mass of the ornament ([tex]m_{1}[/tex]) = 0.9 kg
Length of the wire (l) = 1.5 m
Mass of missile ([tex]m_{2}[/tex]) = 0.4 kg
Initial speed of missile ([tex]u_{2}[/tex]) = 12 m/s
r = 1.5 m
According to the law of conservation of momentum,
[tex]p_{i} = p_{f}[/tex]
[tex]m_{1}u_{1} + m_{2}u_{2} = (m_{1} + m_{2})v[/tex]
Putting the given values into the above formula as follows.
[tex]m_{1}u_{1} + m_{2}u_{2} = (m_{1} + m_{2})v[/tex]
[tex]0.9 \times 0 + 0.4 \times 12 = (0.9 + 0.4)v[/tex]
0 + 4.8 = 1.3v
v = 3.69 m/s
Now, the centrifugal force produced is calculated as follows.
[tex]F_{c} = (m_{1} + m_{2}) \times \frac{v^{2}}{r}[/tex]
= [tex](0.9 + 0.4) \times \frac{(3.69)^{2}}{1.5}[/tex]
= 11.80 N
Hence, tension in the wire is calculated as follows.
T = [tex]F_{c} + (m_{1} + m_{2})g[/tex]
= [tex]11.80 N + (0.9 + 0.4) \times 9.8[/tex]
= 24.54 N
Thus, we can conclude that tension in the wire immediately after the collision is 24.54 N.
The tension in the wire after collision is 24.54 N.
The given parameters;
- mass of the ornament = 0.9 kg
- radius of the wire, r = 1.5 m
- mass of the missile = 0.4 kg
- initial speed of the missile = 12 m/s
Apply principle of conservation of linear momentum to determine the final velocity of the system after collision;
[tex]m_1 u_1 + m_2u_2 = v(m_1 + m_2)\\\\0.9(0) + 0.4(12) = v(0.9 + 0.4)\\\\4.8= 1.3v\\\\v = \frac{4.8}{1.3} \\\\v = 3.69 \ m/s[/tex]
The tension in the wire after collision is calculated as follows;
[tex]T = F_c + W\\\\T = ma_c + mg\\\\T = m(a_c + g)\\\\T = (m_1 + m_2)(\frac{v^2}{r} + g)\\\\T = (0.9 + 0.4)(\frac{3.69^2}{1.5} + 9.8)\\\\T = (1.3)(9.08 +9.8)\\\\T = 24.54 \ N[/tex]
Learn more here:https://brainly.com/question/13778504