Respuesta :
Answer:
(a). The final velocity is 1.78 m/s.
(b). The lost kinetic energy is 266.13 J.
Explanation:
Given that,
Mass of first skater = 60 kg
Mass of second skater = 75.0 kg
Initial velocity = 4.00 m/s
(a). We need to calculate the final velocity
Using conservation of momentum
[tex]m_{1}u_{1}+m_{2}u_{2}=(m_{1}+m_{2})v[/tex]
Put the value into the formula
[tex]60\times4.00+75.0\times0=(60+75.0)v[/tex]
[tex]v=\dfrac{60\times4.00}{60+75}[/tex]
[tex]v=1.78\ m/s[/tex]
The final velocity is 1.78 m/s.
(b). We need to calculate the lost kinetic energy
Using formula of kinetic energy
[tex]\Delta E=E_{2}-E_{1}[/tex]
[tex]\Delta E=\dfrac{1}{2}(m_{1}u_{1}^2+m_{2}u_{2}^2)-\dfrac{1}{2}(m_{1}+m_{2})v^{2}[/tex]
[tex]\Delta E=\dfrac{1}{2}(60\times4^2)-\dfrac{1}{2}\times(60+75)\times1.78^2[/tex]
[tex]\Delta E=266.13\ J[/tex]
Hence, (a). The final velocity is 1.78 m/s.
(b). The lost kinetic energy is 266.13 J.
a. The final velocity should be considered as the 1.78 m/s.
b. The lost kinetic energy should be considered as the 266.13 J.
Conservation of momentum:
Since
Mass of first skater = 60 kg
Mass of second skater = 75.0 kg
Initial velocity = 4.00 m/s
a.
We know that
[tex]mm1v1 + m2v2 = (m1 + v1)v\\\\60*4.00 + 75*0 = (60 + 75)v[/tex]
v = 60 + 4/60 + 75
= 1.78 m/s
b.
[tex]E = 1/2(m1v1^2 + m2v2^2) - 1/2(m1 + vm2)v^2\\\\= 1/2(60*4^2) - 1/2 * (60 + 75)*1.78^2[/tex]
= 266.13 J
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