Respuesta :
Answer:
[tex]v=0.31m/s[/tex]
[tex]K_{Ai}=0.1125J[/tex]
Explanation:
We know that linear momentum must be conserved, so linear momentum at the initial stage (before collision) must be equal to linear momentum at the final stage (after collision): [tex]p_i=p_f[/tex].
We call [tex]m_A[/tex] the mass of cart A, [tex]v_{Ai}[/tex] its velocity before the collision, [tex]m_B[/tex] the mass of cart B, [tex]v_{Bi}[/tex] its velocity before the collision and v the velocity of both together.
Linear momentum at the initial stage is: [tex]p_i=m_Av_{Ai}+m_Bv_{Bi}[/tex]
Linear momentum at the final stage is: [tex]p_f=(m_A+m_B)v}[/tex]
So we have:
[tex]m_Av_{Ai}+m_Bv_{Bi}=(m_A+m_B)v}[/tex]
Which means:
[tex]v=\frac{m_Av_{Ai}+m_Bv_{Bi}}{m_A+m_B}[/tex]
We substitute our values to get:
[tex]v=\frac{(0.9Kg)(0.5m/s)+(0.55Kg)(0m/s)}{(0.9Kg)+(0.55Kg)}=0.31m/s[/tex]
And since the equation for kinetic energy is [tex]K=mv^2/2[/tex] we substitute our values for A at the initial stage:
[tex]K_{Ai}=0.1125J[/tex]
(A)The final velocity of cart B will be 0.3 m/sec.
(B)The energy possessed by the body due to its motion is known as kinetic energy. the initial kinetic energy of cart A will be 0.11255 J.
What is the law of conservation of momentum?
According to the law of conservation of momentum, the momentum of the body before the collision is always equal to the momentum of the body after the collision.
The momentum of the body is given by the product of the mass and velocity of the body.
Momentum before collision
[tex]\rm{P_i = m_av_a+ m_bv_b}[/tex]
Momentum after collision
[tex]\rm{P_f=(m_a+ m_b})V}[/tex]
According to the law of conservation of momentum
Momentum before collision =Momentum after collision
[tex]\rm{ m_av_a+ m_bv_b}=\rm(m_a+ m_b})V}}[/tex]
[tex]\rm V = \frac{\rm{m_av_a+ m_bv_b}}{\rm{(m_a+ m_b})}}[/tex]
[tex]\rm V = \frac{\rm{0.9\times0.5+ 0.55\times 0}}{\rm{(0.99+ 0.55})}}[/tex]
[tex]\rm{V = 0.31 m/sec}[/tex]
Hence the final velocity of the cart B will be 0.3 m/sec.
The kinetic energy of the body is given by,
[tex]\rm{KE = \frac{1}{2}mV^{2} }[/tex]
[tex]\rm{KE = \frac{1}{2}\times0.900 (0.5)^{2}}[/tex]
[tex]\rm{KE = 0.11255 J[/tex]
Hence the initial kinetic energy of cart A will be 0.11255 J
To learn more about the law of conservation of momentum refer;
https://brainly.com/question/1113396
