Respuesta :
Answer:
The percentage of kinetic energy transformed into thermal energy is 33.18%.
Explanation:
Given that,
Initial speed of the two car = 4.0 m/s
Let the mass of the box cars be m.
(a). we need to calculate the final speed of the three coupled boxcars
Using conservation of energy
[tex]m_{1}u_{i}+m_{2}u_{i}=(m_{1}+m_{2})v_{f}[/tex]
Put the value into the formula
[tex]2m\times4.0+0=3m\times v_{f}[/tex]
[tex]v_{f}=\dfrac{2m\times4.0}{3m}[/tex]
[tex]v_{f}=2.67\ m/s[/tex]
The final speed of the three cars is 2.67 m/s.
(b). We need to calculate the initial kinetic energy
Using formula of kinetic energy
[tex]K.E=\dfrac{1}{2}mv^2[/tex]
Put the value into the formula
[tex]K.E_{i}=\dfrac{1}{2}\times2m\times(4.0)^2[/tex]
[tex]K.E_{i}=16m\ J[/tex]
We need to calculate the final kinetic energy
Using formula of kinetic energy
[tex]K.E_{f}=\dfrac{1}{2}\times3m\times(2.67)^2[/tex]
[tex]K.E_{f}=10.69m\ J[/tex]
We need to calculate the loss of kinetic energy
[tex]K.E_{l}=K.E_{i}-K.E_{f}[/tex]
[tex]K.E_{l}=16m-10.69m[/tex]
[tex]K.E_{l}=5.31m\ J[/tex]
We need to calculate the fraction of the cars' initial kinetic energy is transformed into thermal energy
[tex]K.E'=\dfrac{K.E_{l}}{K.E_{i}}[/tex]
[tex]K.E'=\dfrac{5.31m}{16m}[/tex]
[tex]K.E'=0.3318\ J[/tex]
We need to calculate the percentage of kinetic energy transformed into thermal energy
[tex]K.E'=0.3318\times 100[/tex]
[tex]K.E'=33.18\%[/tex]
Hence, The percentage of kinetic energy transformed into thermal energy is 33.18%.
