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Two carts, A and B, are connected by a spring and sitting at rest on a track. Cart A has a mass of 0.4 kg and Cart B has a mass of 0.8 kg. The spring is released and causes the two carts to push off from each other. Which of the following correctly compares the motion and forces acting on the two carts?

A. Cart A experiences a greater force but has the same speed as Cart

B. Cart A experiences a greater force and has a greater speed after the recoil.

C. Both carts experience the same force but Cart A has a greater speed after the recoil.

D. Both carts experience the same force and have the same speed after the recoil.

Respuesta :

onyebuchinnaji

Both carts experience the same force but Cart A has a greater speed after the recoil.

The given parameters;

  • Mass of the cart A = 0.4 kg
  • Mass of the cart B = 0.8 kg

Apply the principle of conservation of linear momentum to determine the velocity of the carts after collision;

[tex]m_Av_0_A\ + m_Bv_0_B = m_Av_f_A \ + m_Bv_f_B\\\\the \ initial \ velocity \ of \ both \ carts = 0\\\\0.4(0) + 0.8(0) = 0.4v_f_A + 0.8v_f_B\\\\0 = 0.4v_f_A + 0.8v_f_B\\\\0.4v_f_A = -0.8v_f_B\\\\v_f_A= \frac{-0.8 v_f_B}{0.4} \\\\v_f_A = - 2 \ v_f_B \ \ m/s[/tex]

According to Newton's third law of motion, action and reaction are equal and opposite. The force exerted on cart A is equal to the force exerted on cart B but in opposite direction.

[tex]F_A = -F_B[/tex]

Thus, the correct statement that compares the motion and forces acting on the two carts is "Both carts experience the same force but Cart A has a greater speed after the recoil."

Learn more about conservation of linear momentum here: https://brainly.com/question/7538238

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